CN114218875A - Acceleration method and device for flow field prediction - Google Patents

Acceleration method and device for flow field prediction Download PDF

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CN114218875A
CN114218875A CN202111517186.4A CN202111517186A CN114218875A CN 114218875 A CN114218875 A CN 114218875A CN 202111517186 A CN202111517186 A CN 202111517186A CN 114218875 A CN114218875 A CN 114218875A
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刘学军
丁子元
吕宏强
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Nanjing University of Aeronautics and Astronautics
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Abstract

The embodiment of the invention discloses an acceleration method and device for flow field prediction, relates to the field of flow field prediction in fluid mechanics research, and can intelligently accelerate the flow field prediction process in a high-order DG numerical format. The invention comprises the following steps: the CFD server receives initial flow field condition data sent by a client; establishing a calculation frame aiming at a flow field, and acquiring training data by using the calculation frame; arranging the training data according to the spatial adjacent relation of each unit in the computational grid, and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework; training the neural network through the training sample set until the prediction precision meets the engineering application requirement; and generating a prediction sample set according to the current flow field condition data, and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.

Description

Acceleration method and device for flow field prediction
Technical Field
The invention relates to the field of flow field prediction in fluid mechanics research, in particular to an acceleration method and device for flow field prediction.
Background
In recent thirty years, along with development and progress of computing power and mathematical algorithms, a Computational Fluid Dynamics (CFD) technology has advanced sufficiently, and design and optimization based on a numerical simulation technology are increasingly popularized, however, a high-precision calculation process of an unsteady flow field is time-consuming, and is a problem to be solved urgently.
The High-order Discontinuous Galerkin (DG) method can obtain High-order precision in units of any geometric shape, and is considered to be one of the most promising technologies for solving the problem. But the method increases the order of the interpolation function in the unit and also increases the actual calculation amount and storage amount of a single unit. Although the unknown degree of freedom required by the high-order discontinuous Galerkin is much less than that of the finite volume method under the condition of obtaining numerical results with equal precision in general, the long-time unsteady calculation amount is still large.
Therefore, how to intelligently accelerate the flow field prediction process in the high-order DG numerical format becomes a problem needing to be researched.
Disclosure of Invention
The embodiment of the invention provides an acceleration method and device for flow field prediction, which can intelligently accelerate the flow field prediction process in a high-order DG numerical format.
In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:
in a first aspect, an embodiment of the present invention provides a method, including:
s1, the CFD server receives initial flow field condition data sent by the client, where the flow field condition data at least includes: the incoming flow attack angle, the incoming flow Mach number and the Reynolds number of the flow field at the initial moment;
s2, establishing a calculation framework for the flow field, and acquiring training data by using the calculation framework, wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information;
s3, arranging the training data according to the spatial adjacent relation of each unit in the computational grid, and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework;
s4, training the neural network through the training sample set until the prediction precision meets the engineering application requirement;
and S5, generating a prediction sample set according to the current flow field condition data, and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
In a second aspect, an embodiment of the present invention provides an apparatus, including:
a receiving module, configured to receive initial flow field condition data sent by a client, where the flow field condition data at least includes: the incoming flow attack angle, the incoming flow Mach number and the Reynolds number of the flow field at the initial moment;
the calculation preparation module is used for establishing a calculation frame for the flow field and acquiring training data by using the calculation frame, wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information;
the preprocessing module is used for arranging the training data according to the spatial adjacent relation of each unit in the computational grid and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework;
the training module is used for training the neural network through the training sample set until the prediction precision meets the engineering application requirement;
and the prediction module is used for generating a prediction sample set according to the current flow field condition data and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
According to the acceleration method and the acceleration device for flow field prediction provided by the embodiment of the invention, a user can input flow field working condition information at a client side. The CFD server constructs a computing framework (compressible or incompressible) after initialization operation, performs numerical simulation by using a high-order DG algorithm, and constructs an overall training sample set for training according to the computing grid and the adjacent relation thereof. And training a hybrid neural network on a GPU (graphics processing Unit) computing power platform to obtain a flow field prediction model, verifying prediction accuracy, adjusting or retraining the model if the accuracy does not meet the engineering application requirement, returning the finally determined network to the CFD server, and calling the network to achieve the purpose of improving the computing efficiency. And returning the intelligent acceleration result meeting the precision requirement of the engineering application to the visual interface of the client. The method is suitable for the industrial application scene of rapidly and accurately acquiring the unsteady flow field.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of an overall logical framework provided by an embodiment of the present invention;
FIG. 2 is a general flow diagram of unsteady flow field prediction modeling for a high order DG numerical format in a particular embodiment;
FIG. 3 is a diagram of a computational grid in an embodiment;
FIG. 4 is a diagram illustrating a grid adjacency in an exemplary embodiment;
FIG. 5 is an overall block diagram of a deep neural network in an exemplary embodiment;
FIG. 6 is a three-dimensional convolution module structure in an exemplary embodiment;
FIG. 7 is a residual network module architecture in an exemplary embodiment;
FIG. 8 is an attention mechanism module configuration in an exemplary embodiment;
FIG. 9 illustrates the location of two designated observation points in the computational grid in an exemplary embodiment;
FIG. 10 is a graph of the relative error of variable u at points P1 and P2 for a particular embodiment;
FIG. 11 is a graph of the relative error of variable v at points P1 and P2 for a particular embodiment;
FIG. 12 is a graph of the relative error of the variable P at points P1 and P2 for a particular embodiment, and it can be seen from FIGS. 10-12 that the indicator of the ordinate MAPE is controlled to be below 0.2%;
FIG. 13 is a schematic diagram of a process flow provided by an embodiment of the present invention;
fig. 14 is a schematic diagram of a device structure according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention. As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
Conventional computational fluid dynamics methods include finite element methods, finite difference methods, finite volume methods. However, for some complicated flow problems, such as turbulence, shock wave, aerodynamic noise, etc., vortex structures, shock wave structures and fine disturbance sound waves of different scales need to be accurately captured, and the actual physical viscosity of the fluid can be covered due to excessive dissipation at low-order precision, so that fine numerical simulation cannot be performed. The high-order DG algorithm adopted in the embodiment belongs to a high-precision algorithm, and the defects are overcome. However, the existing numerical simulation method consumes huge computing resources, and in order to solve this problem, researchers use a reduced order model to improve the computing efficiency, such as a Dynamic Modal Decomposition (DMD) method, a Koopman Operator (Koopman Operator) method, and a intrinsic Orthogonal Decomposition (POD) method. However, the boundary conditions, the real flow field states such as the reynolds number and the like have great influence on the model accuracy of the method, and the reduced-order model has poor robustness and is not suitable for being applied to flow fields under all conditions. The deep learning technology is an efficient function approximation technology and is also applied to the field of flow field prediction in recent years, however, some works still have limitations, that is, a training sample is composed of physical quantities on a limited number of sampling points on a computational grid, and if the physical quantities at all positions in a flow field are obtained, an interpolation method is generally adopted, so that potential errors are caused.
In general, the conventional numerical simulation method consumes a large amount of computing resources, is long in computing time, and occupies a large amount of computing resources, so that the design purpose of the embodiment is to intelligently accelerate the flow field prediction process in the high-order DG numerical format.
The design idea of this embodiment mainly lies in: the method is different from the design idea of working of taking a flow field as an image in the existing scheme and then predicting the flow field through deep learning. In this embodiment, a new modeling manner is designed, and the high-order polynomial coefficients (i.e., the original variables of the high-order discontinuous galileo method) generated in the CFD solution are arranged according to the spatial neighboring relationship of the grid cells, and form sequence data according to the time sequence relationship. Specifically, a feasible novel deep neural network is constructed based on an original data structure of a high-order discontinuous Galerkin method, and a holographic unsteady flow field is obtained by directly predicting an unsteady high-order polynomial coefficient (namely an original unknown number). The invention utilizes the related technology in the field of computer vision to capture the space-time dynamic characteristics in hydrodynamics, and provides a mixed deep neural network to quickly predict flow field information based on the main idea of data driving so as to achieve the purpose of intelligent acceleration.
The invention belongs to the field of flow field prediction in computational fluid dynamics, and particularly relates to intelligent acceleration of unsteady flow field calculation of a high-order intermittent Galerkin method.
An embodiment of the present invention provides an acceleration method for flow field prediction, as shown in fig. 13, including:
and S1, the CFD server receives the initial flow field condition data sent by the client.
Wherein the flow field condition data includes at least: the incoming flow attack angle, incoming flow Mach number and Reynolds number of the flow field at the initial moment. Specifically, after the user logs in the client, the CFD server and the computing platform grant the right corresponding to the user according to the user right level. And then, the CFD server side and the computing platform perform initialization operations including but not limited to allocating resources and binding the resources with login users, storing user operation records and the like. The user may then enter initial conditions at the client needed to calculate the flow field.
And S2, establishing a calculation framework aiming at the flow field, and acquiring training data by using the calculation framework.
Wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information. Specifically, a corresponding control model is constructed at a CFD server side, and high-order polynomial coefficients required by model training and testing are generated by using implicit large vortex simulation based on a high-order DG algorithm.
And S3, arranging the training data according to the spatial adjacent relation of each unit in the computational grid, and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework.
As shown in fig. 3, a schematic diagram of the computational grid designed in this embodiment is shown, wherein a grid cell can be understood as each small cell in fig. 3. Specifically, the computational grid cells in fig. 3 can be equivalently converted into the grid adjacency diagram shown in fig. 4 according to the adjacency relationship between them. In this embodiment, the generated training data are arranged according to the spatial neighboring relationship of the computational grid units, and a training sample set is constructed according to the time sequence relationship.
And S4, training the neural network through the training sample set until the prediction precision meets the engineering application requirement.
And the training sample set is placed on a GPU computational power platform to train the neural network, prediction accuracy verification is carried out, and model adjustment or retraining is carried out if the accuracy does not meet the engineering application requirements. Specifically, the percentage error is controlled to be below 1%, and the predicted flow field cloud picture is not different from the real result visually, so that the prediction precision can be considered to meet the engineering application requirement.
And S5, generating a prediction sample set according to the current flow field condition data, and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
The method includes inputting a small amount of known samples into a neural network after training is completed, and dynamically predicting flow field data of a time period after training, so that the calculation efficiency is improved.
The method can be applied to the field of unsteady flow field prediction, the time efficiency of acquiring the holographic flow field data is obviously improved so as to achieve the purpose of intelligent acceleration, the method has good generalization performance, and a brand-new unsteady flow field prediction modeling idea method is provided for the engineering application field of computational fluid mechanics. The invention comprises the following steps: the user can input the flow field working condition information at the client by himself. The CFD server constructs a control equation (compressible or incompressible) after initialization operation, performs numerical simulation by using a high-order DG algorithm, and constructs an overall training sample set for training according to the computational grid and the adjacent relation thereof. And training a hybrid neural network on a GPU (graphics processing Unit) computing power platform to obtain a flow field prediction model, verifying prediction accuracy, adjusting or retraining the model if the accuracy does not meet the engineering application requirement, returning the finally determined network to the CFD server, and calling the network to achieve the purpose of improving the computing efficiency. And returning the intelligent acceleration result meeting the precision requirement of the engineering application to the visual interface of the client. The method is suitable for the industrial application scene of rapidly and accurately acquiring the unsteady flow field.
In this embodiment, the process of acquiring training data by using the computing framework includes: and carrying out numerical simulation on a control equation (N-S equation) in the calculation framework by adopting an implicit large vortex simulation mode.
Where the first step is the governing equation, and 4 links before the sample set construction, i.e. the step for solving the governing equation, are shown in fig. 2. Specifically, the numerical simulation method adopts Implicit Large Eddy Simulation (ILES). When solving a control equation, the traditional large-vortex simulation method firstly needs to divide the flow into large-scale vortices and small-scale vortices through a filter function. After filtering, a sub-lattice stress tensor is obtained, which is an additional term introduced in the filtering process, similar to the additional eddy viscosity term introduced in the turbulence model of the RANS method. The implicit large vortex simulation is different from the explicit method, the dissipation of a numerical value format in the calculation process is directly used as a sub-lattice model, and an additional model does not need to be built to enable an equation to be closed. The uncertainty caused by the interaction between the filtering truncation error and the numerical error in the large vortex simulation method is avoided.
Then, carrying out space dispersion on the calculation frame by using a discontinuous Galerkin method (DG algorithm), and then carrying out non-constant time advance on the calculation frame by using implicit time dispersion, wherein the iterative calculation is carried out by adopting a Newton method in a single time step. And finally, acquiring the high-order expression coefficient.
The method comprises the steps of firstly utilizing an intermittent Galerkin method to carry out space dispersion on an N-S equation (namely the control model), then adopting an implicit time dispersion mode to finish non-constant time propulsion, wherein a Newton method is adopted to carry out iterative calculation in a single time step, and the generated large linear system is calculated by utilizing a preprocessed GMERS method, so that data required by training, namely a high-order expression coefficient, is obtained.
Specifically, the control equation includes:
Figure BDA0003400148060000081
wherein U represents a conservation variable, t represents a time variable, Fc(U) denotes no viscous flow, U and v denote orthogonal components of velocity,
Figure BDA0003400148060000091
representing a viscous flux.
The conservation variable U in the two-dimensional case is:
Figure BDA0003400148060000092
where ρ represents the pressure at a point in the flow field, u and v represent orthogonal components of velocity, and E represents the unit total energy.
The utilizing of the discontinuous Galerkin method to carry out space dispersion on the computing frame comprises the following steps: carrying out space dispersion on the calculation frame by using a discontinuous Galerkin method, wherein the obtained dispersion form is as follows:
Figure BDA0003400148060000093
Figure BDA0003400148060000094
wherein j is more than or equal to 0 and less than or equal to n, phijIn order to be the basis function(s),
Figure BDA0003400148060000095
in order to introduce the auxiliary variable(s),
Figure BDA0003400148060000096
flux of auxiliary value, omega, introduced by the boundary integral parteThe unit of the presentation is,
Figure BDA0003400148060000097
represents the unit ΩeN denotes the outer normal vector of the cell boundary, UhThe amount of the conservation variable is represented,
Figure BDA0003400148060000098
is the subscript of the viscous numerical flux, j, representing the basis function,
Figure BDA0003400148060000099
Θ-and
Figure BDA00034001480600000910
Θ+values of variables representing the left and right cells of the interface, respectively, F is the integral of the diffusion term inside the cell, ΘhIs an auxiliary variable, σ represents the boundary of the calculation region,
Figure BDA00034001480600000911
is the value of a variable that is,
Figure BDA00034001480600000912
representing the integral of the diffusion term at the cell boundary.
The discrete system for deriving the computational framework from the discrete form is:
Figure BDA00034001480600000913
where M is a global quality matrix, u ═ u1,u2,...,uk,...,uNele]TIs a global degree of freedom vector, ukRepresents the degree of freedom, u, of the unit kk＝[u1,1,u1,2,…,u1,Nd,…,uk,1,…,uk,Nd,…,uNe,1,…,uNe,Nd]TWherein Nele represents the number of global units, Ne, Nd are respectively shownR (u) ═ R, which represents the number of equations in the cell and the degree of freedom of each variable1,R2,...,Rk,…,RNele]TAs a global residual vector, RkRepresenting the residual vector for unit k.
Further, the method also comprises the following steps: by dividing the computational domain by a structured grid, the variable U is conserved inside the grid unith(x, t) is
Figure BDA0003400148060000101
Wherein u isj(t) is the original variable in the form of a higher order coefficient, phij(x) And N is the number of basis functions corresponding to the order of the high-order expression coefficient. The division of the computational domain adopts a structured grid, the computational grid is shown in fig. 3, and the conservation variables are expressed by high-order polynomials in the grid unit:
Figure BDA0003400148060000102
wherein u isj(t) is the original variable in the form of a higher order coefficient, phij(x) N is the number of basis functions corresponding to the order number.
In this embodiment, the process of performing non-constant time advance on the computation framework through implicit time dispersion includes:
residual value item tn+1Calculating the residual value item of the time step, and processing the discrete system of the calculation frame by adopting a backward Euler difference method to obtain:
Figure BDA0003400148060000103
wherein, tn+1Unsteady residual value R of stepeComprises the following steps:
Figure BDA0003400148060000104
at each time step tn+1Solving by Newton iteration until the residual value Re(uk) Infinity approaches 0. A
Specifically, implicit time dispersion is carried out, and a residual value item is taken as tn+1Calculating the time step variable and adopting the direction of the above formulaPost-euler difference method, the following form is obtained:
Figure BDA0003400148060000105
definition of tn+1Unsteady residual value R of stepeComprises the following steps:
Figure BDA0003400148060000106
at each time step tn+1Solving by adopting a Newton iteration method until a residual value R is obtainede(uk) → 0. The method comprises the following specific steps:
u0＝un
Figure BDA0003400148060000107
un+1＝uk+1
wherein, the lambda is a relaxation factor,
Figure BDA0003400148060000111
the jacobian matrix is the k-th newton iteration step equation. The implicit time advance method herein can be divided into three levels. The outermost link is a time step cycle, then a Newton iteration cycle of the above formula, and the innermost link is the solution of a linear equation set. And entering the next Newton cycle after the solution of the innermost linear equation system is converged. Newton cycle up to an unsteady residual value Re(un+1) The number of iteration steps of 0 or Newton is close to kmaxThereafter, the program proceeds to the next time step tn+1And (4) calculating. Thereby obtaining the original variable ujAnd (t), substituting the formula to obtain the physical quantity in each unit in the flow field, and obtaining the holographic flow field information.
Further, the constructing the training sample set according to the time sequence relationship includes:
and uniformly calibrating the flow field information at each moment in a rectangular space with a fixed size. And extracting a calculation conservation variable U in each grid unit in each time step.
Wherein the required interpolation polynomial coefficient is uj(t)(j 1.. 10), each mesh cell contains 40 higher-order expression coefficients when a 3-order format is employed. Specifically, the flow field information at each time can be uniformly calibrated in a rectangular space with a fixed size (the size of the rectangular space depends on the structure of the computational grid). Within a single time step, the coefficient obtained by the iterative calculation of the Newton method is taken according to the following method: namely, the interpolation polynomial coefficient U (composed of four components) required for calculating the conservation variable U is extracted in each unitj(t) (j ═ 1.. 10), each unit contains 40 higher order expression coefficients in the case of a 3 rd order format. Therefore, three-dimensional data is adopted to represent flow field information at each moment, and finally the data are arranged according to time sequence to obtain an overall data set.
Training a neural network through the training sample set, including: and establishing a three-dimensional convolution neural network module of the neural network and a deep residual convolution network module. Embedding a soft attention mechanism module in a last portion of the neural network. Randomly initializing network parameters and inputting the training set into the neural network. The weight of each neuron is corrected by optimizing the weight and the bias coefficient by minimizing a loss function. Wherein the loss function is:
Figure BDA0003400148060000121
Ngrepresenting the total number of training data, lambda represents the regularization coefficient,
Figure BDA0003400148060000122
predicted values, Y, representing a deep neural networkiRepresenting the results of CFD calculations at the same time, w represents a weighting factor,
Figure BDA0003400148060000123
representing the square of the 2-norm of the weighting factor. For example: a three-dimensional convolution neural network module and a deep residual convolution network module can be established firstly; then embedding a soft attention mechanism module called SENET (Squeeze-and-Excitation Networks) into the last part of the whole network; thereafter, the network is randomly initializedParameters and the training data set is input to the network, and the loss function is as follows:
Figure BDA0003400148060000124
wherein N isgRepresenting the total number of training data, lambda represents the regularization coefficient,
Figure BDA0003400148060000125
predicted values, Y, representing a deep neural networkiAnd the second term represents the corresponding CFD calculation result, and is L2 parameter norm penalty, which is also called weight attenuation, so that the learning capability of the model is limited to a certain extent, and the generalization error is reduced instead of the training error.
Finally, the weights and bias coefficients are optimized by minimizing a loss function, i.e., the weights of each neuron are corrected according to error back propagation.
The process for detecting whether the prediction precision meets the engineering application requirements comprises the following steps: converting the result (composed of high-order expression coefficients) after the neural network training into a flow field cloud chart; judging whether the prediction cloud picture meets the precision requirement or not so as to evaluate the prediction capability of the model; if the precision does not meet the engineering application requirement, adjusting the model or retraining the model; and returning the finally determined network to the CFD server, and achieving the purpose of improving the computing efficiency by calling the network. And returning the intelligent acceleration result meeting the precision requirement of the engineering application to the visual interface of the client.
The neural network designed in this embodiment is specifically a hybrid deep neural network, which is composed of modules, including:
(1) a three-dimensional convolution module: three-dimensional convolution acts on a cube formed by a plurality of adjacent frames stacked together, and then a calculation is performed in this cube using a three-dimensional convolution kernel. As shown in fig. 6, the left column is continuous in time, each feature map on the right is connected to two adjacent frames in the previous layer, and the value at each position in the feature map is obtained by performing convolution operation on the same receptive field of three continuous frames in the previous layer, so as to capture dynamic information. In the deep neural network, the value at the point (x, y, z) on the ith layer jth feature map has the mathematical expression:
Figure BDA0003400148060000131
w, H and D in the above formula respectively represent the sizes of three dimensions of width, length and height in a three-dimensional convolution kernel, tanh is a nonlinear activation function,
Figure BDA0003400148060000132
is the value at the (w, h, d) position in the three-dimensional convolution kernel connected to the kth feature map in the previous layer, bijRepresenting the bias parameter.
Assume that L is stacked in total in the three-dimensional convolution module of FIG. 6cThree-dimensional convolutional layers, below which are listed the mathematical expressions between two layers,
Figure BDA0003400148060000133
wherein x(l-1)Which is the input to the l-th layer, f denotes the activation function,
Figure BDA0003400148060000134
is a corresponding three-dimensional convolution operation, WlAnd BlRepresenting the three-dimensional convolution kernel and the bias parameters, respectively.
(2) A residual error network module: the residual error network can well solve the network degradation problem. After the three-dimensional convolution module fully extracts information on a time dimension, a residual error network structure which does not increase extra calculation amount for a network and is easier to train is adopted.
As shown in FIG. 7, each residual block is composed of two activation functions and two-dimensional convolution operations, the mapping in the residual unit is denoted as f, and L is stacked after the three-dimensional convolution blockrThe number of residual units, in the form of,
Figure BDA0003400148060000141
wherein theta islRepresents the set of all parameters available for learning in the ith residual unit,
Figure BDA0003400148060000142
is the input of the l-th residual unit.
(3) An attention mechanism module: the inspiration of attention mechanism comes from the study of human vision, namely, limited visual information processing resources are preferentially allocated to key parts, and irrelevant information is omitted. The effect of neighboring regions in the entire space on the final prediction is not the same, and we attribute this effect to spatial heterogeneity. This is very compatible with the soft attention in the image processing field, and each region is given a parameter which can be learned according to the degree of attention of each region, wherein the parameter is between 0 and 1 and can be differentiated, and the optimal weight can be determined through the forward propagation and backward feedback of the neural network.
In this context, to further enhance the model's capability, a soft attention mechanism module like SENET (Squeeze-and-Excitation Networks) as shown in FIG. 8 is embedded into the last part of the overall network structure to explore and automatically quantify how each region is contributed by features at channel level. The original features are re-calibrated at the channel level by the module.
Fig. 2 shows an overall work flow diagram of the developed method, and implicit large vortex simulation is performed on a control equation to be solved, an N-S equation is subjected to spatial dispersion by using a discontinuous galaogin method, then unsteady time propulsion is completed by adopting an implicit time dispersion mode, wherein iteration calculation is performed by adopting a newton method within a single time step, and a large linear system generated by the method is calculated by using a preprocessed GMERS method, so that data required by training, namely high-order expression coefficients are obtained. And finishing the construction of the training sample set, and then training the neural network until the precision requirement is met.
Two points P1(1.5, 0) and P2(5, 0.5) as shown in fig. 9 were selected in the example to show the prediction accuracy of the time series. Comparing the three physical quantities u, v, p predicted by the deep neural network at the selected position with the real samples to obtain relative Error results as shown in fig. 10-12, wherein the ordinate of the relative Error graph represents the average percent Error (MAPE), and the expression is as follows:
Figure BDA0003400148060000151
in the above formula N represents the total number of data,
Figure BDA0003400148060000152
for the predicted value, y is the corresponding true value calculated by CFD. All the predicted results are well matched with the CFD calculation results. The accumulated error has no obvious influence on the prediction result as the number of steps of the recursive prediction increases. The rationality of each module of the hybrid deep neural network provided by the invention is proved, expected flow field characteristics can be captured, and the prediction of an unsteady flow field is realized.
Table 1 below shows the training and test duration comparison of the developed method for unsteady flow field prediction under two different conditions.
Figure BDA0003400148060000153
TABLE 1
In the aspect of time consumption of calculation, the specific information of CFD calculation and deep network training and testing is shown in table 1 (hardware of CFD calculation is Intel Xeon e 56492.53ghz 4 core parallel, a parallel calculation mode is adopted, hardware of neural network prediction is Intel Xeon Silver 4210R 2.40GHz 40 core parallel, a parallel calculation mode is not adopted), it can be found that 7500s is needed for one cycle of CFD numerical simulation in the second calculation example, and 60s is needed for predicting one cycle based on the unsteady flow field prediction method of the deep learning strategy after training is completed. The time required by model prediction in all the examples is reduced by more than two orders of magnitude, and the calculation cost can be obviously saved.
The embodiment can intelligently accelerate numerical simulation aiming at a high-order DG numerical format, can be used in the fields of computational fluid mechanics and numerical simulation, can improve the time efficiency of flow field system solving, and also improves the utilization rate of computational resources. The traditional high-fidelity computing method has the limiting factors of long computing period and the like, and the holographic flow field is predicted by using a mixed neural network, so that a brand-new deep learning flow field modeling idea is provided for the application field of fluid mechanics. The invention comprises the following steps: the user can input the flow field working condition information at the client by himself. The CFD server constructs a computing framework (compressible or incompressible) after initialization operation, performs numerical simulation by using a high-order DG algorithm, and constructs an overall training sample set for training according to the computing grid and the adjacent relation thereof. And training a hybrid neural network on a GPU (graphics processing Unit) computing power platform to obtain a flow field prediction model, verifying prediction accuracy, adjusting or retraining the model if the accuracy does not meet the engineering application requirement, returning the finally determined network to the CFD server, and calling the network to achieve the purpose of improving the computing efficiency. And returning the intelligent acceleration result meeting the precision requirement of the engineering application to the visual interface of the client. Therefore, not only the distribution of calculation force is considered, but also the calculation precision and efficiency of the flow field can be improved. Therefore, the simulation calculation efficiency and precision in the flow field analysis process can be considered simultaneously, the efficiency of the whole flow field analysis system is improved, the utilization rate of calculation resources is also improved, and the calculation efficiency of each example and the effectiveness of calculation power distribution are improved.
The present embodiment also provides an acceleration apparatus for flow field prediction, as shown in fig. 14, including:
a receiving module, configured to receive initial flow field condition data sent by a client, where the flow field condition data at least includes: the incoming flow attack angle, incoming flow Mach number and Reynolds number of the flow field at the initial moment.
The calculation preparation module is used for establishing a calculation frame for the flow field and acquiring training data by using the calculation frame, wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information.
And the preprocessing module is used for arranging the training data according to the spatial adjacent relation of each unit in the computational grid and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework.
And the training module is used for training the neural network through the training sample set until the prediction precision meets the engineering application requirement.
And the prediction module is used for generating a prediction sample set according to the current flow field condition data and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
According to the acceleration method and the acceleration device for flow field prediction provided by the embodiment of the invention, a user can input flow field working condition information at a client side. The CFD server constructs a computing framework (compressible or incompressible) after initialization operation, performs numerical simulation by using a high-order DG algorithm, and constructs an overall training sample set for training according to the computing grid and the adjacent relation thereof. And training a hybrid neural network on a GPU (graphics processing Unit) computing power platform to obtain a flow field prediction model, verifying prediction accuracy, adjusting or retraining the model if the accuracy does not meet the engineering application requirement, returning the finally determined network to the CFD server, and calling the network to achieve the purpose of improving the computing efficiency. And returning the intelligent acceleration result meeting the precision requirement of the engineering application to the visual interface of the client. The method is suitable for the industrial application scene of rapidly and accurately acquiring the unsteady flow field. The time efficiency of solving the flow field system can be improved, and the utilization rate of computing resources is also improved. The traditional high-fidelity computing method has the limiting factors of long computing period and the like, and the embodiment utilizes the mixed neural network to predict the holographic flow field, thereby providing a brand-new deep learning flow field modeling idea for the application field of fluid mechanics engineering.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the apparatus embodiment, since it is substantially similar to the method embodiment, it is relatively simple to describe, and reference may be made to some descriptions of the method embodiment for relevant points. The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (9)

1. An acceleration method for flow field prediction, comprising:
s1, the CFD server receives initial flow field condition data sent by the client, where the flow field condition data at least includes: the incoming flow attack angle, the incoming flow Mach number and the Reynolds number of the flow field at the initial moment;
s2, establishing a calculation framework for the flow field, and acquiring training data by using the calculation framework, wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information;
s3, arranging the training data according to the spatial adjacent relation of each unit in the computational grid, and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework;
s4, training the neural network through the training sample set until the prediction precision meets the engineering application requirement;
and S5, generating a prediction sample set according to the current flow field condition data, and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
2. The method of claim 1, wherein in the process of obtaining training data by using the computing framework, the method comprises:
carrying out numerical simulation on a control equation in the calculation frame by adopting an implicit large vortex simulation mode;
and carrying out space dispersion on the calculation frame by using a discontinuous Galerkin method, then carrying out non-constant time propulsion on the calculation frame by using implicit time dispersion, and further acquiring the high-order expression coefficient, wherein iterative calculation is carried out by using a Newton method in a single time step.
3. The method of claim 2, wherein the governing equation comprises:
Figure FDA0003400148050000011
wherein U represents a conservation variable, t represents a time variable, Fc(U) denotes no viscous flow, U and v denote orthogonal components of velocity,
Figure FDA0003400148050000012
represents viscous flux;
the conservation variable U in the two-dimensional case is:
Figure FDA0003400148050000021
where ρ represents the pressure at a point in the flow field, u and v represent orthogonal components of velocity, and E represents the unit total energy.
4. The method of claim 3, wherein spatially discretizing the computational framework using a discontinuous Galerkin method comprises:
carrying out space dispersion on the calculation frame by using a discontinuous Galerkin method, wherein the obtained dispersion form is as follows:
Figure FDA0003400148050000022
Figure FDA0003400148050000023
0≤j≤n，φjin order to be the basis function(s),
Figure FDA00034001480500000212
in order to introduce the auxiliary variable(s),
Figure FDA0003400148050000024
flux of auxiliary value, omega, introduced by the boundary integral parteThe unit of the presentation is,
Figure FDA0003400148050000025
represents the unit ΩeN denotes the outer normal vector of the cell boundary, UhThe amount of the conservation variable is represented,
Figure FDA0003400148050000026
is that the viscous numerical flux j represents the subscript of the basis function,
Figure FDA0003400148050000027
Θ-and
Figure FDA0003400148050000028
Θ+the variable values of the left and right cells of the interface are represented, respectively, F represents the integral of the diffusion term inside the cell, thetahRepresenting the auxiliary variables, sigma the calculation region boundaries,
Figure FDA0003400148050000029
the values of the variables are represented by,
Figure FDA00034001480500000210
represents the integral of the diffusion term at the cell boundary;
the discrete system for deriving the computational framework from the discrete form is:
Figure FDA00034001480500000211
where M is a global quality matrix, u ═ u1,u2,...,uk,...,uNele]TIs a global degree of freedom vector, ukRepresents the degree of freedom, u, of the unit kk＝[u1,1,u1,2,…,u1,Nd,…,uk,1,…,uk,Nd,…,uNe,1,…,uNe,Nd]TWhere Nele represents the number of global cells, Ne, Nd represent the number of in-cell equations and the degree of freedom of each variable, respectively, and R (u) ═ R1,R2,...,Rk,…,RNele]TAs a global residual vector, RkRepresenting the residual vector for unit k.
5. The method of claim 4, further comprising:
by dividing the computational domain by a structured grid, the variable U is conserved inside the grid unith(x, t) is
Figure FDA0003400148050000031
Wherein u isj(t) is the original variable in the form of a higher order coefficient, phij(x) And N is the number of basis functions corresponding to the order of the high-order expression coefficient.
6. The method of claim 5, wherein in the process of non-constant time advancing the computation framework through implicit time dispersion, comprising:
residual value item tn+1Calculating the residual value item of the time step, and processing the discrete system of the calculation frame by adopting a backward Euler difference method to obtain:
Figure FDA0003400148050000032
wherein, tn+1Unsteady residual value R of stepeComprises the following steps:
Figure FDA0003400148050000033
at each time step tn+1Solving by Newton iteration until the residual value Re(uk) Infinity approaches 0.
7. The method of claim 6, wherein constructing the training sample set according to a time-series relationship comprises:
uniformly calibrating the flow field information at each moment in a rectangular space with a fixed size;
within each time step, extracting a computation conservation variable U in each grid cell, wherein the required interpolation polynomial coefficient is Uj(t) (j ═ 1.. 10), each grid cell contains 40 higher order expression coefficients when a 3 rd order format is employed.
8. The method of claim 7, wherein training the neural network with the set of training samples comprises:
establishing a three-dimensional convolution neural network module of the neural network and a deep residual convolution network module;
embedding a soft attention mechanism module into a last portion of the neural network;
randomly initializing network parameters and inputting the training set into the neural network;
correcting the weight of each neuron by optimizing the weight and the bias coefficient by minimizing a loss function, wherein the loss function is:
Figure FDA0003400148050000041
Ngrepresenting the total number of training data, lambda represents the regularization coefficient,
Figure FDA0003400148050000042
predicted values, Y, representing a deep neural networkiRepresenting the same phaseThe result of the CFD calculation, w represents a weight coefficient,
Figure FDA0003400148050000043
representing the square of the 2-norm of the weighting factor.
9. An acceleration device for flow field prediction, comprising:
a receiving module, configured to receive initial flow field condition data sent by a client, where the flow field condition data at least includes: the incoming flow attack angle, the incoming flow Mach number and the Reynolds number of the flow field at the initial moment;
the calculation preparation module is used for establishing a calculation frame for the flow field and acquiring training data by using the calculation frame, wherein the training data comprises: flow field information divided according to time and a high-order expression coefficient corresponding to the flow field information;
the preprocessing module is used for arranging the training data according to the spatial adjacent relation of each unit in the computational grid and then constructing a training sample set according to the precedence order relation of the data generated by the computational framework;
the training module is used for training the neural network through the training sample set until the prediction precision meets the engineering application requirement;
and the prediction module is used for generating a prediction sample set according to the current flow field condition data and inputting the prediction sample set into the trained neural network to obtain a prediction result output by the trained neural network.
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