CN109858158A - A kind of method for parameter configuration and system of computational fluid dynamics simulation - Google Patents
A kind of method for parameter configuration and system of computational fluid dynamics simulation Download PDFInfo
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Abstract
A kind of method for parameter configuration of computational fluid dynamics simulation, it include: the experiment value that the parameter of computational fluid dynamics simulation is set, the experimental result data collection of computational fluid dynamics simulation is obtained using the method for simulated experiment, and error evaluation is carried out based on the experimental result data collection, obtain error information；Experiment value, the error information and the simulated experiment result data collection based on the parameter determines error model and performance model；Using the error model and performance model as constraint, the parameter configuration optimal value that computational fluid dynamics simulation is calculated is carried out；The parameter includes mesh-density and discrete order.Technical solution provided by the invention can be configured in high-order computational fluid dynamics simulation based on grid order independent theory configuration parameter, can be accomplished best performance under the premise of meeting required precision, be improved the efficiency of high-order computational fluid dynamics simulation.
Description
Technical field
The present invention relates to computational fluid dynamics simulation calculating, and in particular to a kind of parameter configuration of computational fluid dynamics simulation
Method and system.
Background technique
Fluid Mechanics Computation is a typical cross discipline, it utilizes numerical method, and by computer simulation, to solve
Certainly physics, biology and the Chemical Problem in reality.Compared to traditional test method, in addition at low cost, except high-efficient, meter
Fluid operator mechanical simulation also has the characteristics that flexibly adjustable.For example, in the computational fluid dynamics simulation to aerofoil profile, in order to observe
Phenomenon under different physics operating conditions usually only needs to adjust related to primary condition, boundary condition in Fluid Mechanics Computation code
Parameter；It is more believable in order to obtain as a result, then need to only adjust parameter relevant to simulation precision, usually refined net or
The precision of person's raising discrete scheme.However, in actual engineer application, this flexibility of computational fluid dynamics simulation but by
To many constraints and limitation, such as the performance simulated.
For traditional low order analogy method, in order to improve simulation precision, main means are to increase mesh-density.So
And due to the limitation of hardware platform resource such as memory etc. itself, it is impossible to unlimitedly be encrypted to grid.Generally, right
In one 2 dimension problem, one times of mesh refinement, then the demand of memory is at least doubled；In addition, simulated time also will increase, into
And the efficiency entirely simulated is caused to decline.
Higher-order method refers to the method with the above spatial accuracy of second order.Its compared to low order method, convergence rate faster,
Thus, it is always the hot spot being concerned in Fluid Mechanics Computation field.In the latest 20 years, researchers propose and have developed each
The high-order discrete scheme of kind various kinds, including the continuous finite element of high-order, high-order discontinuous Galerkin, based on the high-order limited of ENO/WENO
Volumetric method, high-order finite difference method etc..It is simulated compared to low order, high-order simulation by adjusting mesh-density in addition to that can control
Outside simulation precision, the precision of simulation can also be changed by adjusting discrete order.Therefore, it in the simulation of actual high-order,
The precision for improving high-order simulation, there are three types of optional approach is general: h encryption, p encryption and hp encryption.Wherein, h encryption method
It is exactly fixed order, grid is encrypted；P encryption refers to that fixed mesh density is constant, is improved by improving discrete order
Simulation precision；And hp encryption is then the combination of h encryption and p encryption, that is, can increase mesh-density and discrete levels simultaneously
It is secondary.
However, high-order, which is simulated, equally faces the trade-off problem simulated between similar precision and performance with low order, also, by
It is more complicated in variable control parameters, it had not only included grid, but also including discrete order, this is particularly problematic.Because of encryption
Grid and the discrete order of raising can bring the raising of precision, while also can all bring the decline for solving the time, then, in reality
Simulation in, how to carry out parameter configuration, that is, select suitable mesh-density and discrete order, could make simulation result exist
While meeting required precision, solving the time is also most short, the difficulty faced of having at high-order computational fluid dynamics simulation
Topic.
During computational fluid dynamics simulation, actual engineer application is given in contradictory relation between performance and precision
Bring very big challenge.For low order method, most common solution is the unrelated test of grid, that is, passes through test at least 3
Analog result under grid m1, m2 and m3 that set density gradually increases, if the result under these grid scales meets centainly
Constraint condition, for example all reached preset required precision, then select the smallest m1 of grid scale as final simulation lattice.
And high-order is simulated, the unrelated test of traditional grid is no longer applicable in, and is generally used based on experience or didactic method
Determine the parameter configuration of simulation, but this method needs to be repeated trial and error, time cost is high, ease for use is poor.
Summary of the invention
When in order to solve the high-order computational fluid dynamics simulation in the presence of the prior art between performance and required precision
Equilibrium problem, the present invention provide the method for parameter configuration and system of a kind of computational fluid dynamics simulation.
Present invention provide the technical scheme that
A kind of method for parameter configuration of computational fluid dynamics simulation, it is improved in that including:
The experiment value of the parameter of computational fluid dynamics simulation is set, Fluid Mechanics Computation is obtained using the method for simulated experiment
The experimental result data collection of simulation, and error evaluation is carried out based on the experimental result data collection, obtain error information；
Experiment value, the error information and the simulated experiment result data collection based on the parameter determines error model
And performance model；
Using the error model and performance model as constraint, the ginseng that computational fluid dynamics simulation is calculated is carried out
Number configuration optimal value；
The parameter includes mesh-density and discrete order.
Preferably, the experiment parameter of computational fluid dynamics simulation is set, it is described to be simulated using the method for simulated experiment
Result data collection, and error evaluation is carried out based on the analog result data set, obtain error information, comprising:
The experiment value of the parameter of computational fluid dynamics simulation is set, carries out simulated experiment and obtains simulated experiment result data
Collection；
Based on the simulated experiment result data collection, the error evaluation of simulated experiment is carried out, error information is obtained.
Preferably, described to be based on the simulated experiment result data collection, the error evaluation simulated obtains error information
Include:
When the true solution of computational fluid dynamics simulation is known, it is based on the simulated experiment result data collection, using error
Calculation formula calculates error information；
When the really solution of computational fluid dynamics simulation is unknown, based on the simulated experiment result data collection using standard
Richardson extrapolation method or innovatory algorithm based on Richardson extrapolation method calculate error information.
Experiment value, the error information and the simulated experiment result data collection for being preferably based on the parameter determine
Error model and performance model, comprising:
The calculating of error model and performance model is set separately in the experiment value of parameter based on computational fluid dynamics simulation
Formula；
According to the error information and the simulated experiment result data collection, respectively to the error model and performance model
In calculating formula assessed, determine the coefficient in the error model and performance model calculating formula；
The coefficient in calculating formula and the calculating formula based on error model determines error model；Based on performance model
Formula and the coefficient of the calculating formula determine performance model.
Preferably, according to the error information and the simulated experiment result data collection, respectively to the error model and
Calculating formula in performance model carries out assessment
It is assessed according to the error information and the simulated experiment result data collection using least square method or optimization method
Coefficient in the error model and performance model.
Preferably, described using the error model and performance model as constraint, it carries out that calculating fluid is calculated
The parameter configuration optimal value of mechanical simulation, comprising:
According to the error model and performance model, one in two parameters of the mesh-density and discrete order is fixed
The office of the simulated experiment of computational fluid dynamics simulation is calculated in the value of parameter, the search space of another parameter of traversal search
Portion's optimal solution；
According to the locally optimal solution, the search space of the parameter of preset parameter value described in traversal search, until traversal institute
The search space for stating two parameters of mesh-density and discrete order, is calculated the complete of the simulated experiment of computational fluid dynamics simulation
Office's optimal solution, using globally optimal solution as the optimal value of the parameter configuration of computational fluid dynamics simulation.
A kind of parameter configuring system of computational fluid dynamics simulation, including error module, model module and optimal solution module；
Error module: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, is obtained using the method for simulated experiment
The experimental result data collection of computational fluid dynamics simulation is obtained, and error evaluation is carried out based on the experimental result data collection, is obtained
Error information；
Model module: for experiment value, the error information and the simulated experiment result data based on the parameter
Collect and determines error model and performance model；
Optimal solution module: for carrying out that calculating is calculated using the error model and performance model as constraint
The parameter configuration optimal value of fluid Simulation；
The parameter includes mesh-density and discrete order.
Preferably, the error module includes: experiment submodule and assessment submodule；
Experiment submodule: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, carries out simulated experiment and obtains mould
Draft experiment result data collection；
It assesses submodule: for being based on the simulated experiment result data collection, carrying out the error evaluation of simulated experiment, obtain
Error information.
Preferably, the model module includes: calculating formula submodule, coefficient submodule and model submodule；
Calculating formula submodule: for the experiment value of the parameter based on computational fluid dynamics simulation, error model is set separately
With the calculating formula of performance model；
Coefficient submodule: it is used for according to the error information and the simulated experiment result data collection, respectively to the mistake
Calculating formula in differential mode type and performance model is assessed, and determines the coefficient in the error model and performance model calculating formula；
Model submodule: error model is determined for the coefficient in the calculating formula and the calculating formula based on error model；
The coefficient of calculating formula and the calculating formula based on performance model determines performance model.
Preferably, the optimal solution module includes: the first traversal submodule and the second traversal submodule；
First traversal submodule: for according to the error model and performance model, the fixed mesh-density and discrete
The value of a parameter in two parameters of order, calculating fluid force is calculated in the search space of another parameter of traversal search
Learn the locally optimal solution of the simulated experiment of simulation；
Second traversal submodule: for according to the locally optimal solution, the parameter of preset parameter value described in traversal search
Search space, until the search space of traversal two parameters of the mesh-density and discrete order, is calculated calculating fluid force
The globally optimal solution for learning the simulated experiment of simulation, using globally optimal solution as the optimal of the parameter configuration of computational fluid dynamics simulation
Value.
Compared with prior art, the invention has the benefit that
Technical solution provided by the invention is determined using analogue experiment method in high-order computational fluid dynamics simulation and is calculated
The mesh-density parameter and discrete levels subparameter of fluid Simulation, can be in the efficiency for improving high-order computational fluid dynamics simulation
In the case where, meet required precision and reaches best performance.
The parameter configuration that high-order is simulated is converted to constrained optimization problem by technical solution provided by the invention, gets rid of tradition
Heuristic bring it is uncertain, improve the ease for use of high-order computational fluid dynamics simulation.
Technical solution provided by the invention is versatile, is applicable in the very strong versatility simulation of various high-orders and calculates.
Detailed description of the invention
Fig. 1 is the method for parameter configuration schematic diagram of computational fluid dynamics simulation of the invention；
Fig. 2 is the parameter configuring system schematic diagram of computational fluid dynamics simulation of the invention；
Fig. 3 is the parameter configuration flow chart of computational fluid dynamics simulation of the invention.
Specific embodiment
For a better understanding of the present invention, the contents of the present invention are done further with example with reference to the accompanying drawings of the specification
Explanation.
Embodiment 1:
A kind of method for parameter configuration of computational fluid dynamics simulation, as shown in Figure 1, comprising:
Step 1: the experiment value of the parameter of computational fluid dynamics simulation being set, is obtained using the method for simulated experiment and calculates stream
The experimental result data collection of mechanics simulation, and error evaluation is carried out based on the experimental result data collection, obtain error information；
Step 2: experiment value, the error information and the simulated experiment result data collection based on the parameter, which determines, to be missed
Differential mode type and performance model；
Step 3: using the error model and performance model as constraint, carrying out that Fluid Mechanics Computation mould is calculated
Quasi- parameter configuration optimal value；
The parameter includes mesh-density and discrete order.
Step 1: the experiment parameter of computational fluid dynamics simulation is set, and the method using simulated experiment obtains simulation knot
Fruit data set, and error evaluation is carried out based on the analog result data set, obtain error information, comprising:
The experiment value of the parameter of computational fluid dynamics simulation is set, carries out simulated experiment and obtains simulated experiment result data
Collection；
Based on the simulated experiment result data collection, the error evaluation of simulated experiment is carried out, error information is obtained.
Specifically, described to be based on the simulated experiment result data collection, the error evaluation simulated obtains error information
Include:
When the true solution of computational fluid dynamics simulation is known, it is based on the simulated experiment result data collection, using error
Calculation formula calculates error information；
When the really solution of computational fluid dynamics simulation is unknown, based on the simulated experiment result data collection using standard
Richardson extrapolation method or innovatory algorithm based on Richardson extrapolation method calculate error information.
Step 2: experiment value, the error information and the simulated experiment result data collection based on the parameter, which determines, to be missed
Differential mode type and performance model, comprising:
The calculating of error model and performance model is set separately in the experiment value of parameter based on computational fluid dynamics simulation
Formula；
According to the error information and the simulated experiment result data collection, respectively to the error model and performance model
In calculating formula assessed, determine the coefficient in the error model and performance model calculating formula；
The coefficient in calculating formula and the calculating formula based on error model determines error model；Based on performance model
Formula and the coefficient of the calculating formula determine performance model.
Specifically, according to the error information and the simulated experiment result data collection, respectively to the error model and
Calculating formula in performance model carries out assessment
It is assessed according to the error information and the simulated experiment result data collection using least square method or optimization method
Coefficient in the error model and performance model.
Step 3: it is described using the error model and performance model as constraint, it carries out that calculating fluid force is calculated
Learn the parameter configuration optimal value of simulation, comprising:
According to the error model and performance model, one in two parameters of the mesh-density and discrete order is fixed
The office of the simulated experiment of computational fluid dynamics simulation is calculated in the value of parameter, the search space of another parameter of traversal search
Portion's optimal solution；
According to the locally optimal solution, the search space of the parameter of preset parameter value described in traversal search, until traversal institute
The search space for stating two parameters of mesh-density and discrete order, is calculated the complete of the simulated experiment of computational fluid dynamics simulation
Office's optimal solution, using globally optimal solution as the optimal value of the parameter configuration of computational fluid dynamics simulation.
Embodiment 2:
Based on same inventive concept, the present invention also provides a kind of parameter configuring system of computational fluid dynamics simulation,
Include:
A kind of parameter configuring system of computational fluid dynamics simulation, as shown in Fig. 2, include error module, model module and
Optimal solution module；
Error module: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, is obtained using the method for simulated experiment
The experimental result data collection of computational fluid dynamics simulation is obtained, and error evaluation is carried out based on the experimental result data collection, is obtained
Error information；
Model module: for experiment value, the error information and the simulated experiment result data based on the parameter
Collect and determines error model and performance model；
Optimal solution module: for carrying out that calculating is calculated using the error model and performance model as constraint
The parameter configuration optimal value of fluid Simulation；
The parameter includes mesh-density and discrete order.
Specifically, the error module includes: experiment submodule and assessment submodule；
Experiment submodule: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, carries out simulated experiment and obtains mould
Draft experiment result data collection；
It assesses submodule: for being based on the simulated experiment result data collection, carrying out the error evaluation of simulated experiment, obtain
Error information.
Specifically, the assessment submodule: for being based on the simulated experiment result data collection, the mistake of simulated experiment is carried out
Difference assessment, obtaining error information includes:
When the true solution of computational fluid dynamics simulation is known, it is based on the simulated experiment result data collection, using error
Calculation formula calculates error information；
When the really solution of computational fluid dynamics simulation is unknown, based on the simulated experiment result data collection using standard
Richardson extrapolation method or innovatory algorithm based on Richardson extrapolation method calculate error information.
Specifically, the model module includes: calculating formula submodule, coefficient submodule and model submodule；
Calculating formula submodule: for the experiment value of the parameter based on computational fluid dynamics simulation, error model is set separately
With the calculating formula of performance model；
Coefficient submodule: it is used for according to the error information and the simulated experiment result data collection, respectively to the mistake
Calculating formula in differential mode type and performance model is assessed, and determines the coefficient in the error model and performance model calculating formula；
Model submodule: error model is determined for the coefficient in the calculating formula and the calculating formula based on error model；
The coefficient of calculating formula and the calculating formula based on performance model determines performance model.
Specifically, in coefficient submodule, according to the error information and the simulated experiment result data collection using minimum
Square law or optimization method assess the coefficient in the error model and performance model.
Specifically, the optimal solution module includes: the first traversal submodule and the second traversal submodule；
First traversal submodule: for according to the error model and performance model, the fixed mesh-density and discrete
The value of a parameter in two parameters of order, calculating fluid force is calculated in the search space of another parameter of traversal search
Learn the locally optimal solution of the simulated experiment of simulation；
Second traversal submodule: for according to the locally optimal solution, the parameter of preset parameter value described in traversal search
Search space, until the search space of traversal two parameters of the mesh-density and discrete order, is calculated calculating fluid force
The globally optimal solution for learning the simulated experiment of simulation, using globally optimal solution as the optimal of the parameter configuration of computational fluid dynamics simulation
Value.
Embodiment 3,
In numerical simulation, the precision of simulation is generally measured with error.And it is ground in actual engineer application or science
In studying carefully, usually error specifies a threshold value, when the error of realistic simulation is less than or equal to this threshold value, that is, thinks to simulate
Precision reach requirement, this is also the standard of the unrelated verifying of grid of mainstream.For example, it is generally believed that error is less than 10-2When meet
Engineering precision, and to scientific program, the minimum requirements of error is 10-6.After error meets certain required precision, further
Reduce grid spacing, although error can be made to further decrease, on the one hand, the reduction degree of error is very low；Another party
Face, thus bring expense can but sharply increase.Similarly, when discrete order also can change, it should which there are one group of grids
Order configuration, so that the precision of simulation be made to reach requirement.Therefore, it is unrelated as follows to define grid order:
Definition: the simulation all variable for an order p and mesh-density h, with the increase or discrete levels of mesh-density
The relative error e of secondary raising, simulation is gradually decreased, when error is sufficiently small so that no more than a certain given threshold value ∈ (0≤
∈ < 1) when, then claiming analog parameter configuration at this time is that grid order is unrelated.
According to the definition of the unrelated configuration pair of grid-order it is found that it has the property that
Infinite property: for specific threshold ∈, corresponding to grid-order don't care state point have infinite multiple, Suo Youman
The grid order configuration of sufficient e≤∈ is all that grid order is unrelated；
Transitivity: if threshold value ∈1<∈2, then reaching threshold value ∈1The lower all grid orders of limitation are unrelated to be configured also all
It is able to satisfy threshold value ∈2Precision limitation.
According to infinite property, meet the lower unrelated grid order of certain precision limitation configure theoretically exist it is infinite more
It is a.And engineering in practice, in addition to precision, it is also necessary to consider performance factor.Therefore, reach all grid orders of required precision
In unrelated configuration, the unrelated configuration of the minimum grid order of expense is found to being to need key problems-solving.If enabled all full
The unrelated configuration of the grid order of sufficient error threshold ∈ together forms set A, defines one on A and is less than or equal to about expense
Relationship R, R are an ordering relations, and minimal element of the R on set A is the optimal unrelated configuration of grid order.
The detailed process of the method for parameter configuration of computational fluid dynamics simulation according to Fig. 3 as shown in figure 3, carry out detailed below
Explanation.
Step 1: the experiment value of the parameter of computational fluid dynamics simulation being set, is obtained using the method for simulated experiment and calculates stream
The experimental result data collection of mechanics simulation, and error evaluation is carried out based on the experimental result data collection, obtain error information.
Pass through some specifiable lattice h of full simulationiWith order piAnalog result u under configuration1,u2,…,un, wherein uiTable
Show the variable that user is concerned about, it may be pressure, the analogue datas such as different components of speed, it is also possible to be to solve for the time, store
The performance datas such as expense.Generally, should be smaller as far as possible for the mesh-density of simulated experiment, discrete order also should be lower,
And the number i of simulated experiment generally at least needs 2 times namely i >=2, the result of execution is usually shaped like Di(hi,pi,u1,
u2,...,un), i=1,2 ... data set saved.
Based on simulated experiment result data collection, the error evaluation of computational fluid dynamics simulation is carried out.Error is solved by simulation
With the decision simultaneously of true solution.Therefore, be segmented into two kinds of situations to the evaluation of error: one is the problems that true solution is known；
It is another then be really solve it is unknown.For the previous case, simulation error directly can be calculated according to error calculation formula, than
Such as common L2Error formula isWherein uhIndicate that partial differential equation are in a characteristic density
Carry out solving obtained numerical solution on the grid of h, and u*Then indicate the true solution of the original differential equation.However, actual
In simulation process, the true solution of only seldom some problems be it is known, to most problems, especially challenge,
We are difficult to know its true solution.For such issues that, at present relatively mainstream error assessment means using standard
Richardson Extrapolation method and some innovatory algorithms based on this method, such as general Richardson
Extrapolation method mixes Richardson Extrapolation method and Grid Convergence Index
(GCI) method.Here, the process for calculating error is provided by taking standard Richardson Extrapolation method as an example.
The RE method of standard be by Richardson early stage in the 1900's proposed it is a kind of can be from second order accuracy
The method that solution interpolation obtains 4 rank precision solutions.Its essence be by problem to be solved really regard a unknown number as, then according to
Numerical solution of the Solve problems under two sets of different grids, simultaneous obtains an equation group, then solves to equation group, to obtain
The true solution of primal problem.The true solution that f* is primal problem might as well be set, f is two orders of the primal problem at mesh-density h
Value solution, then being tied to form just like ShiShimonoseki vertical:
F*=f+ah2+O(h3)
H will be met2/h1=2Mesh-density h1And h2Under the conditions of numerical solution f1And f2Substituting into above-mentioned formula respectively can obtain:
The higher order term for ignoring three ranks or more in above-mentioned formula, solving the linear equation in two unknowns group can obtain:
In above-mentioned calculating process, if it is considered that more general situation, such as the numerical discretization process for being p to precision, then
It is tied to form just like ShiShimonoseki vertical:
f*=f+aphp+O(hp+1)
At this point, having increased a known variables p newly, in order to solve, three equations Simultaneous Equations together are at least needed.Cause
This, needs three nested grid h1、h2And h3Under numerical solution.In view of the convenience for calculating and simulating, usually selection h1、h2And h3Meet
h1/h2=h2/h3=r, then:
Ignore the higher order term in above-mentioned equation group, solution can obtain:
Above-mentioned formula group is the original equation solved using general Richardson Extrapolation method
Accurate solution can further solve to obtain simulation error in conjunction with the obtained numerical solution of simulation.
Step 2: experiment value, the error information and the simulated experiment result data collection based on the parameter, which determines, to be missed
Differential mode type and performance model；
The error model that computational fluid dynamics simulation is established according to the error information being calculated, according to simulated experiment result
Performance data in data set establishes the performance model of computational fluid dynamics simulation.Generally, by the way of curve matching come
Establish error model and performance model.The essence of curve matching is to come an approximate system using a continuous function namely curve
The discrete data of column, these data may be test result, it is also possible to the sampled result of simulation.It is quasi- to be most commonly used for curve
Closing function is polynomial function, wherein simplest polynomial function is that linear function is as follows:
Y=ax+b
On this basis, it is as follows that quadratic fit function can be obtained in the order for increasing independent variable:
Y=ax2+bx+c；
With cubic fit function:
Y=ax3+bx2+cx+d。
Other than Polynomial curve-fit, more commonly used fitting function further include exponential function, power function and
The complicated functions such as logarithmic function.Application curves are fitted when establishing model, to need to assess the undetermined coefficient in model.One
As, it is solved using least square method or optimization method.Below by taking typical linear function fit as an example, song is given
The specific implementation process of line fitting.
By taking linear function y=ax+b as an example, if discrete data set isBy the abscissa x of discrete pointiSubstitute into mould
Type, acquired results areThen haveWherein, i=1,2 ..., n.Estimated valueWith measured value yiBetween error are as follows:
Error sum of squares of the objective function S between n measurement point and estimated value is shown below:
So, fit procedure is exactly to find suitable coefficient a, b to make objective function S minimum, it may be assumed that
According to extreme value theory, a and b for so that S is reached minimum should meet following relational expression:
Above-mentioned formula is expressed as matrix format, is shown below:
When matrix A is sequency spectrum, X=A-1The least square solution that B is.
Step 3: using the error model and performance model as constraint, carrying out that fluid Simulation is calculated
Parameter configuration optimal value.
Optimal net will be found in conjunction with grid order independent theory according to the error model and performance model having built up
Lattice, order allocation problem are converted into optimization problem.Constraint condition mainly includes two aspects, and one is accuracy constraint, i.e. grid
Order independent theory；Another constraint condition is then the constraint of analog platform own resources, such as the limitation of machine free memory.
The target of optimization be it is unique, i.e., so that the best performance of simulation, therefore this is a typical single-object problem, optimization
Model is shown below:
In formula, h: mesh-density；P: discrete order；g1: the unrelated accuracy constraint of grid order；g2: the money in simulation process
Source constraint；D1: the search space of network density；D2: the search space of discrete order；The unrelated accuracy constraint of grid order and mould
Resource constraint during quasi-.
Wherein,
D1=h ∈ R | 0 < h < 1 }
In formula, R:；
D2={ p ∈ N+|0<p}
In formula, N+:.
Solution to above-mentioned Optimized model, most intuitive method are using searching loop method.By first fixing a decision
Variable, such as discrete order, then by searching for another decision variable, i.e. mesh-density, search space, find and meet
Locally optimal solution under constraint condition；Then, change discrete order, this decision variable is positive integer due to discrete order.Enable p
=p+1 finds locally optimal solution corresponding to new discrete order；Finally, can be obtained after traversal completes all search spaces
To globally optimal solution.
Above-described embodiment explanation, technical solution provided by the invention are real using simulation in high-order computational fluid dynamics simulation
Proved recipe method determines the mesh-density parameter and discrete levels subparameter of computational fluid dynamics simulation, can be before meeting required precision
It puts, accomplishes best performance, improve the efficiency of high-order computational fluid dynamics simulation.
The parameter configuration that high-order is simulated is converted to constrained optimization problem by technical solution provided by the invention, gets rid of tradition
Heuristic bring it is uncertain, improve the ease for use of high-order computational fluid dynamics simulation.
Technical solution provided by the invention is versatile, is applicable in the very strong versatility simulation of various high-orders and calculates, including height
Rank FInite Element, high-order limited volumetric method and interruption Galerkin method.
Obviously, described embodiments are some of the embodiments of the present invention, instead of all the embodiments.Based on the present invention
In embodiment, all other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, shall fall within the protection scope of the present invention.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
The above is only the embodiment of the present invention, are not intended to restrict the invention, all in the spirit and principles in the present invention
Within, any modification, equivalent substitution, improvement and etc. done, be all contained in apply pending scope of the presently claimed invention it
It is interior.
Claims (10)
1. a kind of method for parameter configuration of computational fluid dynamics simulation characterized by comprising
The experiment value of the parameter of computational fluid dynamics simulation is set, computational fluid dynamics simulation is obtained using the method for simulated experiment
Experimental result data collection, and based on the experimental result data collection carry out error evaluation, obtain error information；
Experiment value, the error information and the simulated experiment result data collection based on the parameter determines error model and property
It can model；
Using the error model and performance model as constraint, the parameter for be calculated computational fluid dynamics simulation is matched
Set optimal value；
The parameter includes mesh-density and discrete order.
2. the method for parameter configuration of computational fluid dynamics simulation as described in claim 1, which is characterized in that setting calculates fluid
The experiment parameter of mechanical simulation, the method using simulated experiment obtains analog result data set, and is tied based on the simulation
Fruit data set carries out error evaluation, obtains error information, comprising:
The experiment value of the parameter of computational fluid dynamics simulation is set, carries out simulated experiment and obtains simulated experiment result data collection；
Based on the simulated experiment result data collection, the error evaluation of simulated experiment is carried out, error information is obtained.
3. the method for parameter configuration of computational fluid dynamics simulation as claimed in claim 2, which is characterized in that described based on described
Simulated experiment result data collection, the error evaluation simulated, obtaining error information includes:
When the true solution of computational fluid dynamics simulation is known, it is based on the simulated experiment result data collection, using error calculation
Formula calculation error data；
When the really solution of computational fluid dynamics simulation is unknown, based on the simulated experiment result data collection using standard
Richardson extrapolation method or innovatory algorithm based on Richardson extrapolation method calculate error information.
4. the method for parameter configuration of computational fluid dynamics simulation as described in claim 1, which is characterized in that based on the parameter
Experiment value, the error information and the simulated experiment result data collection determine error model and performance model, comprising:
The calculating formula of error model and performance model is set separately in the experiment value of parameter based on computational fluid dynamics simulation；
According to the error information and the simulated experiment result data collection, respectively in the error model and performance model
Calculating formula is assessed, and determines the coefficient in the error model and performance model calculating formula；
The coefficient in calculating formula and the calculating formula based on error model determines error model；Calculating formula based on performance model
Performance model is determined with the coefficient of the calculating formula.
5. the method for parameter configuration of computational fluid dynamics simulation as claimed in claim 4, which is characterized in that according to the error
Data and the simulated experiment result data collection, carry out assessment packet to the calculating formula in the error model and performance model respectively
It includes:
According to the error information and the simulated experiment result data collection using described in least square method or optimization method assessment
Coefficient in error model and performance model.
6. the method for parameter configuration of computational fluid dynamics simulation as described in claim 1, which is characterized in that described with the mistake
Differential mode type and performance model carry out the parameter configuration optimal value that computational fluid dynamics simulation is calculated respectively as constraint, packet
It includes:
A parameter according to the error model and performance model, in fixed two parameters of the mesh-density and discrete order
Value, the part of the simulated experiment of computational fluid dynamics simulation is calculated most in the search space of another parameter of traversal search
Excellent solution；
According to the locally optimal solution, the search space of the parameter of preset parameter value described in traversal search, until traversing the net
The overall situation of the simulated experiment of computational fluid dynamics simulation is calculated most in the search space of two parameters of lattice density and discrete order
Excellent solution, using globally optimal solution as the optimal value of the parameter configuration of computational fluid dynamics simulation.
7. a kind of parameter configuring system of computational fluid dynamics simulation, which is characterized in that including error module, model module and most
Excellent solution module；
Error module: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, is counted using the method for simulated experiment
The experimental result data collection of fluid operator mechanical simulation, and error evaluation is carried out based on the experimental result data collection, obtain error
Data；
Model module: for based on the parameter experiment value, the error information and the simulated experiment result data collection it is true
Determine error model and performance model；
Optimal solution module: for carrying out that calculating fluid is calculated using the error model and performance model as constraint
The parameter configuration optimal value of mechanical simulation；
The parameter includes mesh-density and discrete order.
8. the parameter configuring system of computational fluid dynamics simulation as claimed in claim 7, which is characterized in that the error module
It include: experiment submodule and assessment submodule；
Experiment submodule: it for the experiment value of the parameter of computational fluid dynamics simulation to be arranged, carries out simulated experiment and obtains simulation in fact
Test result data collection；
It assesses submodule: for being based on the simulated experiment result data collection, carrying out the error evaluation of simulated experiment, obtain error
Data.
9. the parameter configuring system of computational fluid dynamics simulation as claimed in claim 7, which is characterized in that the model module
It include: calculating formula submodule, coefficient submodule and model submodule；
Calculating formula submodule: for the experiment value of the parameter based on computational fluid dynamics simulation, error model and property is set separately
The calculating formula of energy model；
Coefficient submodule: it is used for according to the error information and the simulated experiment result data collection, respectively to the error mould
Calculating formula in type and performance model is assessed, and determines the coefficient in the error model and performance model calculating formula；
Model submodule: error model is determined for the coefficient in the calculating formula and the calculating formula based on error model；It is based on
The coefficient of the calculating formula of performance model and the calculating formula determines performance model.
10. the parameter configuring system of computational fluid dynamics simulation as claimed in claim 7, which is characterized in that the optimal solution
Module includes: the first traversal submodule and the second traversal submodule；
First traversal submodule: for fixing the mesh-density and discrete order according to the error model and performance model
Fluid Mechanics Computation mould is calculated in the value of a parameter in two parameters, the search space of another parameter of traversal search
The locally optimal solution of quasi- simulated experiment；
Second traversal submodule: for according to the locally optimal solution, the search of the parameter of preset parameter value described in traversal search
Space, until the search space of traversal two parameters of the mesh-density and discrete order, is calculated Fluid Mechanics Computation mould
The globally optimal solution of quasi- simulated experiment, using globally optimal solution as the optimal value of the parameter configuration of computational fluid dynamics simulation.
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