CN117473907B - Cartesian grid self-adaptive encryption method based on flow field accompanying equation - Google Patents
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Abstract
The invention provides a Cartesian grid self-adaptive encryption method based on a flow field accompanying equation, which comprises the following steps: generating an initial cartesian grid; setting a global error threshold of the objective function; solving a three-dimensional compressible non-stick flow control equation on the current Cartesian grid; solving a flow field accompanying equation on the current Cartesian grid; pre-encrypting the current Cartesian grid, and calculating a flow field interpolation solution and an accompanying interpolation solution on the Cartesian fine grid by adopting an interpolation method; calculating the accompanying self-adaptive detector value of the current Cartesian grid unit, and marking the current Cartesian grid unit needing encryption; encrypting the Cartesian grid cell to be encrypted; the adaptive encryption process is terminated when the accompanying adaptive detector values of all grid cells meet the set threshold requirements. The method can accurately position the region with larger output function error in the flow field, ensures that grid encryption is performed at the correct position, and effectively avoids grid over-encryption caused by misjudging the encryption region.
Description
Technical Field
The invention relates to the technical field of fluid mechanics calculation methods, in particular to a Cartesian grid self-adaptive encryption method based on a flow field accompanying equation.
Background
The grid adaptive encryption technology is one of effective means for improving the efficiency and accuracy of flow numerical simulation, and aims to improve the calculation accuracy of an output function (lift force, resistance or moment). How to establish reliable adaptation criteria is one of the key issues of grid adaptation.
The core of the adaptive criterion is to construct various adaptive detectors, and different detectors correspond to different grid adaptive encryption methods. At present, a typical method for mainly constructing the self-adaptive detector is a traditional method based on flow field characteristics, and in the method, the discrete error of a region with large variable gradient such as shock waves is considered to be large, and grid encryption is needed. However, not all errors near the flow characteristics will affect the target output function, encryption near the flow characteristics does not mean that the errors of the target output function must be reduced. The method consumes huge calculation amount and can not effectively improve the calculation accuracy of the output function, and is one of main factors for limiting the wide application of the grid self-adaptive method in engineering calculation.
Therefore, a method for indirectly indicating the region with large contribution to the output function error without identifying the flow field features is needed to accurately locate the region with large output function error in the flow field, so as to ensure that the grid encryption is performed at the correct position.
Disclosure of Invention
The invention aims to at least solve one of the technical problems that in the prior art, errors near all flow characteristics can not affect an objective output function, encryption near the flow characteristics does not mean that the errors of the objective output function can be reduced, the typical method for constructing the self-adaptive detector is difficult to accurately locate the region with larger errors of the output function in a flow field, and the calculated amount is huge.
Therefore, the invention provides a Cartesian grid self-adaptive encryption method based on a flow field accompanying equation.
The invention provides a Cartesian grid self-adaptive encryption method based on a flow field accompanying equation, which comprises the following steps:
importing a calculated digital model to generate an initial Cartesian grid;
setting a global error threshold of a Cartesian grid objective function;
solving a three-dimensional compressible non-viscous flow control equation on the current Cartesian grid by adopting a lattice-lattice finite-volume method;
solving a flow field accompanying equation on the current Cartesian grid according to the flow field solution of the three-dimensional compressible non-stick flow control equation;
pre-encrypting the current Cartesian grid to obtain a Cartesian fine grid, and calculating a flow field interpolation solution and an accompanying interpolation solution on the Cartesian fine grid by adopting an interpolation method;
calculating the accompanying self-adaptive detector value of the current Cartesian grid unit, and marking the current Cartesian grid unit needing encryption according to the self-adaptive criterion;
encrypting the marked Cartesian grid cells to be encrypted;
projecting newly added grid points after being split into fine grids onto an object plane to optimize the quality of the grid units of the object plane;
judging whether the accompanying self-adaptive detector values of all grid cells in the current Cartesian grid meet the set threshold requirement, and terminating the self-adaptive encryption process when the accompanying self-adaptive detector values of all grid cells meet the set threshold requirement.
The Cartesian grid self-adaptive encryption method based on the flow field accompanying equation according to the technical scheme of the invention can also have the following additional technical characteristics:
in the above technical solution, the three-dimensional compressible non-stick flow control equation is:
wherein,the solution vector of the expression equation is defined as a flow field conservation variable, namely, a flow field solution obtained by a three-dimensional compressible non-viscous flow control equation; />Convection flux of the flow field in the x, y and z directions respectively; t is time;
the method for solving the three-dimensional compressible non-viscous flow control equation by adopting the lattice-lattice finite volume method on the current Cartesian grid comprises the following steps:
the discrete of the convection flux adopts a Jameson center format of coupling artificial sticky flux, wherein the artificial sticky flux comprises second-order dissipation and fourth-order dissipation, and the time propulsion adopts an explicit four-step Runge-Kutta format.
In the above technical solution, the flow field accompanying equation is:
wherein,the method is characterized in that the method is an accompanying variable on the current Cartesian grid, namely an accompanying solution obtained through a flow field accompanying equation;for virtual time item, ++>For virtual time +.>For the volume of the current cartesian grid cell, +.>Residual errors of flow field accompanying equations on the current Cartesian grid; />Is the residual value of the three-dimensional compressible non-viscous flow control equation on the current Cartesian grid, +.>For the flow field conservation variable on the current Cartesian grid,/for the flow field conservation variable on the current Cartesian grid>Is an objective function on the current Cartesian grid;
the method for solving the flow field accompanying equation on the current Cartesian grid comprises the following steps:
by adding virtual time terms in the flow field accompanying equationPerforming iterative solution, wherein the condition of iterative convergence is residual error of a flow field accompanying equation>Equal to 0;
the discrete of the convection flux adopts a Jameson central format of coupling artificial viscosity, the artificial viscosity flux comprises second-order dissipation and fourth-order dissipation, a time-pushing method is adopted to solve a virtual time item, and the time-pushing method adopts an explicit four-step Runge-Kutta format.
In the above technical solution, the constraint condition that the current cartesian grid is pre-encrypted to obtain the cartesian fine grid includes embedding the fine grid inside the coarse grid;
the interpolation method includes a linear interpolation method or a quadratic polynomial interpolation method.
In the above technical solution, the accompanying adaptive detector values of the current cartesian grid cellThe calculation method of (1) is as follows:
wherein,for the current Cartesian grid cell +.>Adaptive parameters of->Assigning a global error threshold for the cartesian grid objective function to the allowable error for each cartesian grid cell;
designing a self-adaptive criterion according to a principle of reducing residual error items, wherein an error between a flow solution of a fine grid unit obtained by a convergence method and a flow interpolation solution of the fine grid unit obtained by an interpolation method is defined as a first error; defining an error between the accompanying solution of the fine grid unit obtained by the convergence method and the accompanying interpolation solution of the fine grid unit obtained by the interpolation method as a second error;
the current Cartesian grid cellAdaptive parameters of->The calculation method of (1) comprises the following steps:
calculating residual error items of the objective function according to the first error and the second error respectively to obtain a first residual error item and a second residual error item;
taking the average value of the sum of absolute values of the first residual error term and the second residual error term as the current Cartesian grid cellAdaptive parameters of->。
In the technical scheme, the difference between the high-order flow interpolation solution and the low-order flow interpolation solution of the fine grid unit is approximated to be a first error;
and/or approximating the difference between the high and low order concomitant interpolation solutions of the fine grid cells as a second error.
In the above technical solution, the current Cartesian grid cellAdaptive parameters of->The calculation formula of (2) is as follows:
wherein,numbering fine cells +.>Interpolation solution for higher order flows on fine grid cells,/->Interpolation solution for low order flow on fine grid cells,/->For higher order concomitant interpolation on fine grid cells, +.>For low order concomitant interpolation on fine grid cells, +.>To interpolate with low order +.>The residual value of the flow field accompanying equation on the fine grid unit obtained,/->To interpolate solution +.>And solving the residual value of the flow control equation on the fine grid unit.
In the above technical scheme, willGrid cells greater than a set threshold are marked as requiring encryption.
In the above technical scheme, willThe 3-layer neighbor cells of the grid cell that are greater than the set threshold are marked as requiring encryption.
In the above technical solution, the importing the calculated digital-analog, generating the initial cartesian grid includes:
reading in model geometric data and grid generation control parameters;
generating an initial uniform grid according to the control parameters, and establishing a connection relation of initial grid units;
performing geometric self-adaptive encryption on the generated initial grid unit to obtain an initial Cartesian grid;
removing Cartesian grid cells intersecting the digital analog inside the digital analog;
and (3) smoothing the front of the Cartesian grid, and projecting the vertex of the smoothed front to the object plane to generate an object plane grid.
In summary, due to the adoption of the technical characteristics, the invention has the beneficial effects that:
based on a three-dimensional Cartesian grid, a three-dimensional compressible non-stick flow control equation and a three-dimensional discrete flow field accompanying equation, a grid self-adaptive encryption method suitable for a grid-core format finite volume method is provided. The method directly estimates the errors of the output functions (lift force, resistance and moment) by utilizing the accompanying variables by directly establishing the association relation between the errors of the flow field and the errors of the output functions (lift force, resistance and moment). The method can accurately position the region with larger output function error in the flow field, ensures that grid encryption is performed at the correct position, and effectively avoids grid over-encryption caused by misjudging the encryption region.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of a Cartesian grid adaptive encryption method based on a flow field accompanying equation according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an initial uniform grid generated in a Cartesian grid adaptive encryption method based on flow field accompanying equations in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of an initial Cartesian grid established in a Cartesian grid adaptive encryption method based on a flow field accompanying equation according to an embodiment of the present invention;
fig. 4 is a schematic diagram of encrypting a cartesian grid in a cartesian grid adaptive encryption method based on a flow field accompanying equation according to an embodiment of the invention.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. It should be noted that, in the case of no conflict, the embodiments of the present application and the features in the embodiments may be combined with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as described herein, and therefore the scope of the present invention is not limited to the specific embodiments disclosed below.
A cartesian grid adaptive encryption method based on a flow field accompanying equation provided according to some embodiments of the present invention is described below with reference to fig. 1 to 4.
Some embodiments of the present application provide a cartesian grid adaptive encryption method based on a flow field accompanying equation.
As shown in fig. 1, a first embodiment of the present invention proposes a cartesian grid adaptive encryption method based on a flow field accompanying equation, which includes steps S1 to S9.
S1, importing and calculating a digital model to generate an initial Cartesian grid.
In some embodiments, the initial Cartesian grid generation process includes the steps of:
s11, reading in model geometric data and grid generation control parameters;
s12, generating an initial uniform grid according to the control parameters, and establishing a connection relation of initial grid units, wherein the generated initial uniform grid is shown in fig. 2;
s13, performing geometric self-adaptive encryption on the generated initial grid unit to obtain an initial Cartesian grid, as shown in FIG. 3;
s14, deleting Cartesian grid cells intersecting the digital analog inside the digital analog;
s15, smoothing the front of the Cartesian grid, projecting the vertex of the smoothed front to an object plane, and generating an object plane grid.
It will be appreciated that the above manner of generating the initial cartesian grid is only an example given in this embodiment, and that a person skilled in the art may add or subtract steps to the above method as needed to generate the initial cartesian grid.
S2, setting a global error threshold of the Cartesian grid objective functionThe method comprises the steps of carrying out a first treatment on the surface of the Specifically, the cartesian grid objective function may be at least one of a lift force calculation function, a drag force calculation function, a moment calculation function, or other mechanical calculation functions, where the objective function is used to perform hydrodynamic calculation on the target object, and in this embodiment, the specific content of the objective function is not limited, and only a global error threshold of the objective function is set, where the global error threshold may be understood as a maximum allowable error of a global calculation result of the objective function.
S3, solving a three-dimensional compressible non-viscous flow control equation on the current Cartesian grid by adopting a lattice-lattice finite-volume method; specifically:
the three-dimensional compressible non-stick flow control equation is:
wherein,the solution vector of the expression equation is defined as a flow field conservation variable, namely, a flow field solution obtained by a three-dimensional compressible non-viscous flow control equation; />Convection flux of the flow field in the x, y and z directions respectively; t is time.
In some embodiments, the solving the three-dimensional compressible non-stick flow control equation on the current Cartesian grid using a lattice-format finite volume method comprises: the discrete of the convection flux adopts a Jameson center format of coupling artificial sticky flux, wherein the artificial sticky flux comprises second-order dissipation and fourth-order dissipation, and the time propulsion adopts an explicit four-step Runge-Kutta format. In one embodiment, in the three-dimensional compressible non-stick flow control equation solving process, the far field boundary uses a non-reflective boundary condition and the object plane boundary uses a non-transmissive boundary condition.
S4, solving a flow field accompanying equation on the current Cartesian grid according to flow field solution of the three-dimensional compressible non-stick flow control equation; specifically: the flow field accompanying equation is:
wherein,the method is characterized in that the method is an accompanying variable on the current Cartesian grid, namely an accompanying solution obtained through a flow field accompanying equation;for virtual time item, ++>For virtual time +.>For the volume of the current cartesian grid cell, +.>Residual errors of flow field accompanying equations on the current Cartesian grid; />Is the residual value of the three-dimensional compressible non-viscous flow control equation on the current Cartesian grid, +.>The flow field conservation variable on the current Cartesian grid is the flow field solution on the current Cartesian grid obtained through the step S3; />Is the objective function on the current cartesian grid.
Note that, the superscript T in the present disclosure represents the transpose operator of the matrix.
Wherein, for the stability and the robustness of the solution of the flow field accompanying equation, a virtual time term is added in the flow field accompanying equationPerforming iterative solution, wherein the condition of iterative convergence is residual error of a flow field accompanying equation>Equal to 0, then there is:
and (3) solving a flow field accompanying equation by adopting the same discrete method as the three-dimensional compressible non-stick flow control equation in the step (S3). Specifically, in a flow field accompanying equation, the discrete of the convection flux adopts a Jameson central format of coupling artificial viscosity, the artificial viscosity flux comprises second-order dissipation and fourth-order dissipation, a virtual time item is solved by adopting a time-pushing method, and the time-pushing adopts an explicit four-step range-Kutta format. In one embodiment, in the flow field accompanying equation solving process, a far field boundary adopts a non-reflection boundary condition; the object plane boundary determining method comprises the following steps: firstly, calculating to obtain an internal accompanying solution of the flow field, and then solving an equation describing the relation between the object plane accompanying solution and the internal accompanying solution of the flow field.
Wherein, jameson center format is a term of art, correspondingly interpreted as Jameson center format; the explicit four-step Runge-Kutta format is a term of art and is correspondingly interpreted as an explicit fourth-order Dragon-Kutta format.
S5, pre-encrypting the current Cartesian grid to obtain a Cartesian fine grid, and calculating a flow field interpolation solution and an accompanying interpolation solution on the Cartesian fine grid by adopting an interpolation method; in some embodiments, the pre-encryption is by: dividing a Cartesian grid unit into eight equal fine grid units by adopting a method of uniformly dividing in three coordinate directions of x, y and z, wherein the encryption result is shown in figure 4; it will be appreciated that the terms "coarse" and "fine" as indicated in this disclosure are relative concepts, with the grid cells before encryption being defined as coarse grid cells and the grid cells after encryption being defined as fine grid cells. Specifically, the fine grid is embedded in the coarse grid as constraint conditions for pre-encrypting the current Cartesian grid to obtain the Cartesian fine grid, and the interpolation method can adopt a linear interpolation method or a quadratic polynomial interpolation method.
S6, calculating the accompanying self-adaptive detector value of the current Cartesian grid cell, and marking the current Cartesian grid cell needing encryption according to the self-adaptive criterion.
Wherein the global error of the objective functionI.e. global error of the objective function is represented by the computable error term +.>And residual error term->The self-adaptive criterion is designed according to the principle of reducing the residual error term, and the calculation accuracy of the objective function is improved by uniformly encrypting the local current Cartesian grid unit to reduce the residual error term.
In particular, error terms can be calculatedThe calculation formula of (2) is as follows:
in some embodiments, the flow solution for fine grid cells using a convergence method is solvedFlow interpolation solution to fine grid cells determined by interpolation method>The error between is defined as first error +.>The method comprises the steps of carrying out a first treatment on the surface of the Accompanying solution of fine grid cells obtained by convergence method>Accompanying interpolation solution with fine grid cells obtained by interpolation methodThe error between is defined as second error +.>；
According to the first error respectivelyAnd second error->Calculating a residual error term of the objective function to obtain a first residual error term and a second residual error term;
wherein according to the first errorA calculation formula for calculating a residual error term of the objective function, namely a first residual error term is:
according to the second errorA calculation formula for calculating a residual error term of the objective function, namely a second residual error term is:
wherein,is the residual value of the flow control equation on the fine grid cell,/->Is the residual of the accompanying equation on the fine grid cell.
Can be used forIt is understood that the flow solution of fine grid cells obtained by means of the convergence methodNamely, the flow solution obtained by the method in the step S3 is the concomitant solution of the fine grid cells obtained by the convergence method +.>Namely, the flow interpolation solution of the fine grid cells obtained by the interpolation method is the concomitant solution obtained by the method in the step S4>And the concomitant interpolation solution of the fine grid cells determined by interpolation method>Namely, the flow field interpolation solution and the concomitant interpolation solution obtained in the step S5.
However, solving the flow solution directly on fine grid cellsAnd corresponding concomitant solution->The computational cost required is high, so in some embodiments, the difference between the high and low order interpolation is used to replace the error between the convergence solution and the interpolation solution on the fine grid cells, specifically:
approximating a difference between the high and low order flow interpolation solutions of the fine grid cells as a first error; and approximating the difference between the high and low order concomitant interpolation solutions of the fine grid cells to a second error. The corresponding formula is as follows:
wherein,interpolation solution for higher order flows on fine grid cells,/->Interpolation solution for low order flow on fine grid cells,/->For higher order concomitant interpolation on fine grid cells, +.>For low order companion interpolation solutions on fine grid cells.
After determining the first residual error term and the second residual error term, taking the average value of the sum of absolute values of the first residual error term and the second residual error term as the current Cartesian grid cellAdaptive parameters of->. Wherein the current Cartesian grid cell is calculated +.>Adaptive parameters of->The current Cartesian grid cell must be traversed at that time>All fine grid cells involved->Then the current Cartesian grid cell +.>Adaptive parameters of->The calculation formula of (2) is as follows:
wherein,to interpolate with low order +.>The residual value of the flow field accompanying equation on the fine grid unit obtained,/->To interpolate solution +.>And solving the residual value of the flow control equation on the fine grid unit.
The accompanying adaptive detector values of the current Cartesian grid cell are based on the principle of error equal distributionThe calculation method of (1) is as follows:
wherein,for the current Cartesian grid cell +.>Adaptive parameters of->The allowable error assigned to each Cartesian grid cell for the global error threshold of the Cartesian grid objective function, i.e.>，/>Is the total number of cells of the current Cartesian grid, < >>A global error threshold for the cartesian grid objective function set in step S2.
Setting the set threshold value of the accompanying adaptive detector value of the current Cartesian grid cell to 1, ifMarking the grid cell as requiring encryption; if->The grid cell is marked as not requiring encryption.
In some embodiments, to avoid grid transition non-smoothness problems caused by excessive size differences between adjacent Cartesian grid cells, the method includesThe 3-layer neighboring cells of the mesh cell to be encrypted having a value greater than 1 are also marked as mesh cells to be encrypted.
S7, encrypting the marked Cartesian grid cells to be encrypted; the encryption mode is as follows: a Cartesian grid cell is split into eight equal fine grid cells by adopting a method of evenly splitting in the x, y and z coordinate directions, and the encryption result is shown in figure 4.
And S8, projecting newly added grid points after being split into fine grids onto an object plane, and optimizing the quality of the object plane grid units of the Cartesian fine grids obtained in the step S7. Ensuring the compatibility of the Cartesian grid and the object plane.
S9, circulating the steps S3-S8, judging whether the accompanying self-adaptive detector values of all grid cells in the current Cartesian grid meet the set threshold requirement, and stopping circulating when the accompanying self-adaptive detector values of all grid cells meet the set threshold requirement, so as to complete the self-adaptive encryption process.
In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A Cartesian grid self-adaptive encryption method based on a flow field accompanying equation is characterized by comprising the following steps:
importing a calculated digital model to generate an initial Cartesian grid;
setting a global error threshold of a Cartesian grid objective function;
solving a three-dimensional compressible non-viscous flow control equation on the current Cartesian grid by adopting a lattice-lattice finite-volume method;
solving a flow field accompanying equation on the current Cartesian grid according to the flow field solution of the three-dimensional compressible non-stick flow control equation;
pre-encrypting the current Cartesian grid to obtain a Cartesian fine grid, and calculating a flow field interpolation solution and an accompanying interpolation solution on the Cartesian fine grid by adopting an interpolation method;
calculating the accompanying self-adaptive detector value of the current Cartesian grid unit, and marking the current Cartesian grid unit needing encryption according to the self-adaptive criterion;
encrypting the marked Cartesian grid cells to be encrypted;
projecting newly added grid points after being split into fine grids onto an object plane to optimize the quality of the grid units of the object plane;
judging whether the accompanying self-adaptive detector values of all grid cells in the current Cartesian grid meet the set threshold requirement, and terminating the self-adaptive encryption process when the accompanying self-adaptive detector values of all grid cells meet the set threshold requirement;
the three-dimensional compressible non-stick flow control equation is:
wherein,the solution vector of the expression equation is defined as a flow field conservation variable, namely, a flow field solution obtained by a three-dimensional compressible non-viscous flow control equation; />Convection flux of the flow field in the x, y and z directions respectively; t is time;
the method for solving the three-dimensional compressible non-viscous flow control equation by adopting the lattice-lattice finite volume method on the current Cartesian grid comprises the following steps:
the discrete of the convection flux adopts a Jameson central format of coupling artificial viscosity, the artificial viscosity flux comprises second-order dissipation and fourth-order dissipation, and the time propulsion adopts an explicit four-step Runge-Kutta format;
the flow field accompanying equation is:
wherein,the method is characterized in that the method is an accompanying variable on the current Cartesian grid, namely an accompanying solution obtained through a flow field accompanying equation;for virtual time item, ++>For virtual time +.>Is the volume of the current cartesian grid cell; />Residual errors of flow field accompanying equations on the current Cartesian grid; />Is the residual value of the three-dimensional compressible non-viscous flow control equation on the current Cartesian grid, +.>For the flow field conservation variable on the current Cartesian grid,/for the flow field conservation variable on the current Cartesian grid>Is the objective function on the current cartesian grid.
2. The method of adaptive encryption of a cartesian grid based on a flow field accompanying equation according to claim 1, wherein the method of solving the flow field accompanying equation on the current cartesian grid comprises:
by adding virtual time terms in the flow field accompanying equationPerforming iterative solution, wherein the condition of iterative convergence is residual error of a flow field accompanying equation>Equal to 0;
the discrete of the convection flux adopts a Jameson central format of coupling artificial viscosity, the artificial viscosity flux comprises second-order dissipation and fourth-order dissipation, a time-pushing method is adopted to solve a virtual time item, and the time-pushing method adopts an explicit four-step Runge-Kutta format.
3. The adaptive encryption method of the cartesian grid based on the flow field accompanying equation according to claim 1, wherein the constraint condition that the current cartesian grid is pre-encrypted to obtain the cartesian fine grid comprises embedding the fine grid inside the coarse grid;
the interpolation method includes a linear interpolation method or a quadratic polynomial interpolation method.
4. The method of adaptive encryption of a cartesian grid based on flow field equations according to claim 1, wherein the current cartesian grid cell's accompanying adaptive detector valuesThe calculation method of (1) is as follows:
wherein,for the current Cartesian grid cell +.>Adaptive parameters of->Assigning a global error threshold for the cartesian grid objective function to the allowable error for each cartesian grid cell;
designing a self-adaptive criterion according to a principle of reducing residual error items, wherein an error between a flow solution of a fine grid unit obtained by a convergence method and a flow interpolation solution of the fine grid unit obtained by an interpolation method is defined as a first error; defining an error between the accompanying solution of the fine grid unit obtained by the convergence method and the accompanying interpolation solution of the fine grid unit obtained by the interpolation method as a second error;
the current Cartesian grid cellAdaptive parameters of->Is a calculation method package of (a)The method comprises the following steps:
calculating residual error items of the objective function according to the first error and the second error respectively to obtain a first residual error item and a second residual error item;
taking the average value of the sum of absolute values of the first residual error term and the second residual error term as the current Cartesian grid cellAdaptive parameters of->。
5. The adaptive encryption method of a cartesian grid based on a flow field accompanying equation according to claim 4, wherein the difference between the high and low order flow interpolation solutions of the fine grid cells is approximated as a first error;
and/or approximating the difference between the high and low order concomitant interpolation solutions of the fine grid cells as a second error.
6. The method for adaptive encryption of a cartesian grid based on a flow field accompanying equation according to claim 5, wherein the current cartesian grid cellAdaptive parameters of->The calculation formula of (2) is as follows:
wherein,numbering fine cells +.>Interpolation solution for higher order flows on fine grid cells,/->Interpolation solution for low order flow on fine grid cells,/->For higher order concomitant interpolation on fine grid cells, +.>For low order concomitant interpolation on fine grid cells, +.>To interpolate with low order +.>The residual value of the flow field accompanying equation on the fine grid unit obtained,/->To interpolate solution +.>And solving the residual value of the flow control equation on the fine grid unit.
7. The adaptive encryption method of Cartesian grids based on flow field adjoint equations according to claim 4, wherein the method is to be used forGrid cells greater than a set threshold are marked as requiring encryption.
8. The adaptive encryption method of Cartesian grids based on flow field adjoint equations according to claim 7, wherein the method is to be used forThe 3-layer neighbor cells of the grid cell that are greater than the set threshold are marked as requiring encryption.
9. The method of adaptive encryption of a cartesian grid based on a flow field accompanying equation according to claim 1, wherein the importing the computational digital-to-analog, generating the initial cartesian grid comprises:
reading in model geometric data and grid generation control parameters;
generating an initial uniform grid according to the control parameters, and establishing a connection relation of initial grid units;
performing geometric self-adaptive encryption on the generated initial grid unit to obtain an initial Cartesian grid;
removing Cartesian grid cells intersecting the digital analog inside the digital analog;
and (3) smoothing the front of the Cartesian grid, and projecting the vertex of the smoothed front to the object plane to generate an object plane grid.
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