CN105975645B - A kind of aircraft flow field of region containing shock wave quick calculation method based on multistep - Google Patents
A kind of aircraft flow field of region containing shock wave quick calculation method based on multistep Download PDFInfo
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Abstract
The present invention proposes a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep, flow field is estimated by POD-RBF method first, flow field precision is further increased secondly by POD-ROM method, then corrects the zonule containing shock wave, finally obtains the flow field of aerofoil profile.The multistep method for solving being made of above step realizes the calculating of transonic flow field in conjunction with the POD model established.The method overcome Computational fluid mechanics numerical simulations to need the drawbacks of taking considerable time, can be realized high-fidelity comprising shock wave flow field and calculates, and solves the problems, such as flow field huge number to be asked in engineer application and computational efficiency is low.
Description
Technical field
The present invention relates to a kind of aircraft flow field fast solution methods, more particularly to a kind of flow field containing shock wave region
Fast solution method belongs to applied aerodynamics research field.
Background technique
In aerodynamic scope, the quick and precisely solution in aircraft flow field is always the most important thing of research work, especially
It is that the flow field calculation containing shock wave region is paid special attention to greater need for researcher.And the speed of more and more Flight Vehicle Designs
Degree range is in transonic speed with supersonic speed region, and even hypersonic region, this just inevitably generates shock wave, flowing
Become extremely complex.
Although the high-fidelity Flow Field Calculation based on high-precision physical model, that is, Fluid Mechanics Computation
(Computational Fluid Dynamics, CFD) numerical simulation, may be implemented the accurate solution of aircraft complex flowfield,
But need to expend a large amount of computing resource, especially (aircraft is in different operating conditions in the flow field huge number of required solution
Under aerodynamic characteristic, aircraft Preliminary design or the optimization design of shape etc.), the time for needing to expend is in practical engineering applications
It tends not to be received.
In order to improve the efficiency of aircraft Flow Field Calculation, (Proper Orthogonal is decomposed in conjunction with Proper Orthogonal
Decomposition, POD) agent model (response surface model, Kriging model and radial basis function model etc.) method and
Reduced-order model (Reduced Order Model, ROM) method of governing equation comes into being and obtains certain development.Relatively
Mature two methods, one is by radial basis function (Radial Basis Function, RBF) model in conjunction with POD
POD-RBF method；One is the model order reductions (POD-ROM) by governing equation in conjunction with POD.
The specific practice that POD-RBF method is applied to the prediction of aircraft flow field is: being calculated by experiment or CFD and obtains flight
Flow field under device difference operating condition (including the even multiple variables of height, the angle of attack, Mach number, angle of rudder reflection, geometric shape), which is used as, adopts
Sample snapshot set decomposes to obtain POD base to snapshot set Proper Orthogonal, and each sampling snapshot is projected to POD base, and (POD base can
With truncation) on, a series of corresponding POD base system numbers are obtained, then can set up with operating condition/POD base by RBF agent model
Coefficient is the POD-RBF model of input/output.For any work condition state in duty parameter space, foundation can be passed through
POD-RBF model calculate solve.POD-RBF method is compared, POD-ROM method exists the flow field variable drop in governing equation
On subspace by a small number of POD bases, one group of solution base system can be converted by originally complicated nonlinear partial differential equation
The dimension of several nonlinear ordinary differential equations, governing equation known variables substantially reduces, and gained numerical result is in low-dimensional
The optimal solution found in space is also more in line with actual physics problem.Although occupying more computing resources than POD-RBF method,
But compared with solving original governing equation, the calculating time is greatly reduced.
It is worth noting that, although POD is used to approximate non-linear problem, it must be appreciated that POD itself is one linear
Process, for smooth flow field regions, the flow field calculation result of the available higher fidelity of POD-RBF method, the side POD-ROM
The flow field calculation result of method is more accurate, but when there are two methods when shock problems to ask in the flow field in shock wave region for flow field regions
Solution accuracy all substantially reduces, and POD-ROM method even occurs being difficult to convergent situation.
Summary of the invention
The object of the present invention is to provide a kind of aircraft flow field fast solution methods, and the method overcome Fluid Mechanics Computations
Numerical simulation needs the drawbacks of taking considerable time, can be realized the high-fidelity comprising shock wave flow field and calculates, solves engineering and answer
The flow field huge number to be asked in and the low problem of computational efficiency.
The technical solution of the present invention is as follows:
A kind of aircraft flow field of region containing shock wave quick calculation method based on multistep, it is characterised in that: including with
Lower step:
Step 1: determine operating condition design space:
The flight parameter of the aircraft of analytical calculation as needed, obtains the sample of aerocraft flying parameter design space n
Point xi, i=1,2 ..., n；
Step 2: the flow field sampling solution w of each sample point in obtaining step 1i, i=1,2 ... n, and by all n sample points
Flow field sampling solution building sampling snapshot matrix
Step 3: POD decomposition is carried out to the sampling snapshot matrix A that step 2 obtains:
Step 3.1: calculating the spatial correlation matrix R, R=A of n × n rankHA；
Step 3.2: the eigenvalue matrix Λ and eigenvectors matrix V of solution room correlation matrix R；
Step 3.3: calculating POD basal orientation moment matrix Φ=AV Λ-1/2；Wherein basal orientation moment matrixφiFor POD
Base vector；
Step 3.4: calculating the base system matrix number X of sampling snapshot matrix Ar, Xr=ΦHA；Wherein base system matrix numberxriFor corresponding flow field sampling solution wiPOD base system number；
Step 4: establishing the RBF agent model of flow field sampling solution POD base system number are as follows:
Wherein xrTo need the aerocraft flying parameter design point x of analytical calculation corresponding, exported by RBF agent model
POD base system number；Radial base interpolation coefficient matrix
Radial distance rkj=r (| | xk-xj||,θj), θjFor width parameter, r () is radial basis function；
And according to formula wrbf=Φ xrIt calculates and predicts Flow Field Solution w under the design point x obtained by RBF agent modelrbf；
Step 5: extracting the eigenvalue λ of spatial correlation matrix Ri, in i=1,2 ... n, value maximum to n-thwBig feature
Value, and the nwThe sum of a characteristic value is greater than precision threshold；Obtain the nwThe corresponding POD base vector φ of a characteristic valuej', j=1,2 ...
nw；
Step 6: the n obtained according to step 5wThe corresponding POD base vector φ of a characteristic valuej', obtain under design point x wait ask
Flow field w projects to POD base vector φj' go up expression formulaWhereinFor the POD base system to be asked of corresponding design point x
Number xr' j-th of element value；
Step 7: will w expression formula in flow field be askedFlow field control equation is substituted into, stream field governing equation carries out
It is discrete, it obtains with POD base system number x to be askedr' be variable residual error governing equation R (Φ 'wxr′；X)=0, wherein
Step 8: using gauss-newton method to residual error governing equation R (Φ 'wxr′；X) it=0 is solved:
Step 8.1: residual error governing equation is projected on the test space L by one group of base Ψ；It obtains containing nwIt is a
The static determinacy equation group Ψ of unknown quantityTR(Φ′wxr′；X)=0, wherein Ψ=J Φ 'w, J is Jacobian matrix；
Step 8.2: to formula
ΨTJkΦ′wpk=-ΨTRk
It is iterated solution, obtains POD base system number xr′；Wherein k=1 ..., K are Newton iteration step, and K is determined by convergence
It is fixed, pkWithRespectively kth step iteration when POD base system number increment and Jacobian matrix, αkIt is in pkIn the direction of search
Step-length,For initial value, by formulaIt obtains；
Step 8.3: according to POD base system number xr', obtain the flow field w under design point xrom=Φ 'wxr′；
Step 9: the CFD amendment of local flow field:
Using the residual error R of the last one iteration step in step 8 as foundation, the mesh point for selecting residual error to be greater than given threshold is carried out
CFD amendment: with wromAs first field, the mesh point for calling CFD fluid diagnosis to be greater than given threshold to residual error is solved,
His mesh point flow field value remains unchanged and as solution boundary condition；Stop solving when residual error R drops to given threshold or less；
Step 10: combining the flow field under design point x that the flow field of step 9 local correction is obtained with step 8, designed
Point x final Flow Field Solution.
Further preferred embodiment, a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep,
It is characterized by: obtaining aerocraft flying parameter design space sample point using Latin hypercube experimental design method in step 1
xi, i=1,2 ..., n.
Further preferred embodiment, a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep,
It is characterized by: using the flow field sampling solution w of each sample point in CFD fluid diagnosis obtaining step 1 in step 2i, i=1,
2…n。
Further preferred embodiment, a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep,
It is characterized by: width parameter in step 4dmaxIt is empty for aerocraft flying parameter design in step 1
Between maximum Euclidean distance between middle sample point.
Further preferred embodiment, a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep,
It is characterized by: radial basis function r () uses gauss of distribution function in step 4:D is Euclidean distance.
Further preferred embodiment, a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep,
It is characterized by: in step 9, using the residual error R of the last one iteration step in step 8 as foundation, using Domain Decomposition Method, selection
The region that the mesh point that residual error is greater than given threshold forms is as the modified region of needs；To need the grid in modified region from
It is individually taken out in former grid, with wromAs first field and boundary condition, call CFD fluid diagnosis to the modified region of needs
Grid individually solves, and stops solving when residual error R drops to given threshold or less.
Beneficial effect
Beneficial effects of the present invention embody as follows:
1, present method solves the quick of extensive operating condition aircraft flow field in engineer application to accurately calculate.
2, POD-RBF method for POD-ROM method provides the receipts that first field can accelerate reduced-order model POD-ROM in this method
Speed is held back, and quickly accurately calculating for low speed flow field (without shock wave region) may be implemented in conjunction with (Two-step) in two methods.
3, the application of Region Decomposition technology can will be applied to Two-step method and the shock wave region of smooth domain
CFD approach combines, final to realize that transonic speed or the quick of supersonic flow field accurately calculate；By big to whole flow field residual values
Mesh point be marked, reapply CFD solution also can achieve similar effect.
Additional aspect and advantage of the invention will be set forth in part in the description, and will partially become from the following description
Obviously, or practice through the invention is recognized.
Detailed description of the invention
Above-mentioned and/or additional aspect of the invention and advantage will become from the description of the embodiment in conjunction with the following figures
Obviously and it is readily appreciated that, in which:
Fig. 1 aircraft multistep quick calculation method flow diagram
The c-type grid chart of Fig. 2 two dimension example NACA0012 aerofoil profile
Fig. 3 sampling point conditions distribution schematic diagram
The grid and the position view in original mesh for the CFD correcting region that Fig. 4 Region Decomposition obtains
The pressure profiles versus of Fig. 5 distinct methods schemes
(it be multistep fast solution method, dotted line is Two- that wide dotted line is CFD result, solid line to Fig. 6 mach line contrast schematic diagram
Step method)
Symbol description is as follows in figure:
X/c is aerofoil profile dimensionless x coordinate；Y/c is the dimensionless y-coordinate of aerofoil profile；Variable Ma indicates Mach number；Variables A OA
Indicate the angle of attack；CPFor airfoil surface pressure coefficient；POD-RBF is the radial base interpolation method based on POD；POD-ROM be based on
The model order reduction of POD；Two-step is the method that POD-RBF and POD-ROM are combined；Multistep is based on multistep
Aircraft flow field quick calculation method.
Specific embodiment
The embodiment of the present invention is described below in detail, the embodiment is exemplary, it is intended to it is used to explain the present invention, and
It is not considered as limiting the invention.
The aircraft flow field quick calculation method flow chart such as Fig. 1 institute of region containing shock wave based on multistep in the present embodiment
Show, Transonic Flowss is glued as example using the nothing around NACA0012 aerofoil profile, the present invention is described in further detail in conjunction with attached drawing.
Step 1: determine operating condition design space:
The flight parameter of the aircraft of analytical calculation as needed, obtains the sample of aerocraft flying parameter design space n
Point xi, i=1,2 ..., n；The flight parameter can be selected from flying height, Mach number, angle of attack etc..
In the present embodiment, for given NACA0012 aerofoil profile, flight parameter is selected as Mach number Ma and angle of attack AOA, uses
Latin hypercube experimental design method uniform sampling obtains aerocraft flying parameter design space sample point xi=[AOAi Mai]T,
Angle of attack AOA is 2 °, 3 °, 4 ° and 5 ° respectively, and Mach number Ma is 0.74,0.76,0.78 and 0.80 respectively, then sampled point xi, i=
Fig. 3 is shown in the number n=16 of 1,2 ..., n, sampling operating condition distribution.
Step 2: the flow field sampling solution w of each sample point in obtaining step 1i, i=1,2 ... n, and by all n sample points
Flow field sampling solution building sampling snapshot matrixThe above various middle n is the number of sampled point, then matrix A has n
Column, the dimension N of each column is CFD is calculated under sampling point conditions flow field mesh point number and each mesh point flow field variable multiplies
Product.
Using the flow field sampling solution w of each sample point in CFD fluid diagnosis obtaining step 1 in the present embodimenti, i=1,
2…n.The solution in flow field uses a c-type grid, shares 193 × 57 mesh points, sees Fig. 2.For two dimension without viscous mixed flow
Dynamic and CFD fluid diagnosis uses the finite volume method based on the lattice heart, then has 4 conservation variables [ρ, ρ u, ρ v, ρ E].Each
The dimension N of flow field sampling solution is the flow field mesh point number and each mesh point flow field variable that CFD is calculated under sampling point conditions
Product.Sampling snapshot matrix is deconstructed by these discrete samplingsThen A is the matrix of N × n.
Step 3: POD decomposition being carried out to the sampling snapshot matrix A that step 2 obtains, POD mould is established in engineer application
Type, POD model include following data: a) all sampled points in operating condition design space；B) POD base vector and its corresponding feature
Value；C) each flow field sampling solution projects to corresponding base system number (POD base system number) on POD base.Establishing solution procedure, (H is square as follows
The conjugate transposition of battle array):
Step 3.1: calculating the spatial correlation matrix R, R=A of n × n rankHA；
Step 3.2: the eigenvalue matrix Λ and eigenvectors matrix V, A of solution room correlation matrix RHAV=V Λ；
Step 3.3: calculating POD basal orientation moment matrix Φ=AV Λ-1/2；Wherein basal orientation moment matrixφiFor POD
Base vector；POD base vector φiWith the eigenvalue λ of RiIt corresponds；
Step 3.4: calculating the base system matrix number X of sampling snapshot matrix Ar, Xr=ΦHA；Wherein base system matrix numberxriFor corresponding flow field sampling solution wiPOD base system number.
Step 4: applying POD-RBF method, predict just field wrbf:
The RBF agent model that solution POD base system number is sampled according to POD model foundation flow field, i.e., to sample operating condition/POD base system
Number is input/output, then for a certain aerocraft flying parameter design point x for needing analytical calculation in operating condition design space,
Corresponding prediction operating condition POD base system number can be obtained using the agent model of construction:
Wherein xrTo need the aerocraft flying parameter design point x of analytical calculation corresponding, exported by RBF agent model
POD base system number；Radial base interpolation coefficient matrix
Radial distance rkj=r (| | xk-xj||,θj), θjFor width parameter, width parameter is taken
dmaxFor the maximum Euclidean distance in step 1 in aerocraft flying parameter design space between sample point, r () is radial basis function,
Using gauss of distribution function:D is Euclidean distance；Then according to formula wrbf=Φ xrCalculating passes through RBF
Flow Field Solution w is predicted under the design point x that agent model obtainsrbf。
Below step 5 to step 9 applies POD-ROM method, further corrects to obtain Flow Field Solution wrom:
Step 5: extracting the eigenvalue λ of spatial correlation matrix Ri, in i=1,2 ... n, value maximum to n-thwBig feature
Value, and the nwThe sum of a characteristic value is greater than precision threshold；Obtain the nwThe corresponding POD base vector φ of a characteristic valuej', j=1,2 ...
nw。
The present embodiment take POD base phase close information capacity be 99.8%, then when use nwWhen=12 POD bases, characteristic value it
Just account for 99.8% or more.
Step 6: the n obtained according to step 5wThe corresponding POD base vector φ of a characteristic valuej', obtain under design point x wait ask
Flow field w projects to POD base vector φj' go up expression formulaWhereinFor the POD base system to be asked of corresponding design point x
Number xr' j-th of element value.
Step 7: will w expression formula in flow field be askedFlow field control equation is substituted into, stream field governing equation carries out
It is discrete, it obtains with POD base system number x to be askedr' be variable residual error governing equation R (Φ 'wxr′；X)=0, wherein
The present embodiment flow field control equation uses the ODE of the discrete conservation form of compressible Navier-Stokes equations halfIt will w expression formula in flow field be askedFlow field control equation is substituted into, is obtainedIt is discrete to time term progress, consider that the approximate shceme form residual equation at a certain moment is (fixed
In normal situation, time-derivative item is not considered), it obtains with POD base system number x to be askedr' be variable residual error governing equation R (Φ 'wxr′；X)=0, the number of equation group will be far longer than the number of unknown quantity base system number, be an over-determined systems, have N number of non-
Linear equation, nwGauss-newton method solution can be used in a unknown quantity (POD base system number).
Step 8: using gauss-newton method to residual error governing equation R (Φ 'wxr′；X) it=0 is solved:
Step 8.1: residual error governing equation is projected on the test space L by one group of base Ψ；It obtains containing nwIt is a
The static determinacy equation group Ψ of unknown quantityTR(Φ′wxr′；X)=0, wherein Ψ=J Φ 'w, J is Jacobian matrix；
Step 8.2: to formula
ΨTJkΦ′wpk=-ΨTRk
It is iterated solution, obtains POD base system number xr′；Wherein k=1 ..., K are Newton iteration step, and K is determined by convergence
It is fixed, pkWithRespectively kth step iteration when POD base system number increment and Jacobian matrix, αkIt is in pkIn the direction of search
Step-length,For initial value, by formulaIt obtains；
Step 8.3: according to POD base system number xr', obtain the flow field w under design point xrom=Φ 'wxr′。
So far, it obtains the non-linear reduced-order model equation (POD-ROM) based on POD and solves mode, obtained with POD-RBF
The prediction w arrivedrbfAs first fieldCan make POD-ROM iterative steps reduce and compared with rapid convergence, precision further increases.
Step 9: the CFD amendment of local flow field:
Using the residual error R of the last one iteration step in step 8 as foundation, the mesh point for selecting residual error to be greater than given threshold is carried out
CFD amendment: with wromAs first field, the mesh point for calling CFD fluid diagnosis to be greater than given threshold to residual error is solved,
His mesh point flow field value remains unchanged and as solution boundary condition；Stop solving when residual error R drops to given threshold or less.
Region Decomposition (Domain Decomposition, DD) method can also be used, residual error is selected to be greater than given threshold
Mesh point composition region as needing modified region；The grid in modified region will be needed individually to take from former grid
Out, with wromAs first field and boundary condition, CFD fluid diagnosis is called individually to solve the grid for needing modified region, when
Residual error R stops solving when dropping to given threshold or less.As shown in figure 4, the left side is the grid schematic diagram of correcting region, the right is
Position view of the correcting region in original mesh.For the region, first field is by POD-ROM method solving result wromIt provides,
Boundary is docked with corresponding w in regionromSolution as boundary condition, then solved using CFD solver, so that residual error drops to
It is suitable with the residual error of whole flow field CFD solving result of comparison.
Step 10: combining the flow field under design point x that the flow field of step 9 local correction is obtained with step 8, designed
Point x final Flow Field Solution.
The present embodiment passes through POD-RBF method first and estimates flow field, further increases flow field secondly by POD-ROM method
Then precision corrects the zonule containing shock wave, finally obtain the flow field of aerofoil profile.The multistep solution side being made of above step
Method realizes the calculating of transonic flow field in conjunction with the POD model established.
The surface pressure distributions of distinct methods compares as shown in figure 5, the as can be seen from the figure aircraft stream based on multistep
Field quick calculation method (Multistep) fits like a glove with CFD result, and in addition two methods (POD-RBF and the side Two-step
Method) it is only capable of capturing shock exterior domain.The mach line that Fig. 6 gives distinct methods compares, and it is base that wide dotted line, which is CFD result, solid line,
In aircraft quick calculation method, the dotted line of multistep be POD-ROM and POD-RBF combination method (Two-step method), the figure
The aircraft flow field quick calculation method based on multistep is further illustrated to the validity for solving the flow field containing shock wave.
Table 1 gives the calculated performance of distinct methods, n in table1And n2Respectively indicate the use of POD-RBF, POD-ROM process
Number (the n of POD base1=n, n2=nw), n3Indicate CFD correcting region gridding dimension.As seen from table: a) when the introducing side POD-RBF
When method provides initial value for POD-ROM method, Newton iteration step number drops to 2 from 7, and computational efficiency improves 3.5 times, and POD-RBF
Method itself calculates time-consuming (only 0.19s) and can be ignored compared to POD-ROM time-consuming；B) compared to CFD method for solving,
Aircraft flow field quick calculation method efficiency based on multistep improves about 9 times.
The calculated performance of 1 distinct methods of table compares
Although the embodiments of the present invention has been shown and described above, it is to be understood that above-described embodiment is example
Property, it is not considered as limiting the invention, those skilled in the art are not departing from the principle of the present invention and objective
In the case where can make changes, modifications, alterations, and variations to the above described embodiments within the scope of the invention.
Claims (5)
1. a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep, it is characterised in that: the following steps are included:
Step 1: determine operating condition design space:
The flight parameter of the aircraft of analytical calculation as needed, obtains the sample point x of aerocraft flying parameter design space ni,i
=1,2 ..., n；
Step 2: the flow field sampling solution w of each sample point in obtaining step 1i, i=1,2 ... n, and by the stream of all n sample points
Quarry sampling solution building sampling snapshot matrix
Step 3: POD decomposition is carried out to the sampling snapshot matrix A that step 2 obtains:
Step 3.1: calculating the spatial correlation matrix R, R=A of n × n rankHA；
Step 3.2: the eigenvalue matrix Λ and eigenvectors matrix V of solution room correlation matrix R；
Step 3.3: calculating POD basal orientation moment matrix Φ=AV Λ-1/2；Wherein basal orientation moment matrixφiFor POD basal orientation
Amount；
Step 3.4: calculating the base system matrix number X of sampling snapshot matrix Ar, Xr=ΦHA；Wherein base system matrix number
xriFor corresponding flow field sampling solution wiPOD base system number；
Step 4: establishing the RBF agent model of flow field sampling solution POD base system number are as follows:
Wherein xrTo need the aerocraft flying parameter design point x of analytical calculation corresponding, the POD base exported by RBF agent model
Coefficient；Radial base interpolation coefficient matrix
Radial distance rkj=r (| | xk-xj||,θj), θjFor width parameter, r () is radial basis function；
Width parameterdmaxFor in step 1 in aerocraft flying parameter design space between sample point
Maximum Euclidean distance；
And according to formula wrbf=Φ xrIt calculates and predicts Flow Field Solution w under the design point x obtained by RBF agent modelrbf；
Step 5: extracting the eigenvalue λ of spatial correlation matrix Ri, in i=1,2 ... n, value maximum to n-thwBig characteristic value, and
The nwThe sum of a characteristic value is greater than precision threshold；Obtain the nwThe corresponding POD base vector φ ' of a characteristic valuej, j=1,2 ... nw；
Step 6: the n obtained according to step 5wThe corresponding POD base vector φ ' of a characteristic valuej, obtain the flow field to be asked under design point x
W projects to POD base vector φ 'jUpper expression formulaWherein x 'r jFor the POD base system number to be asked of corresponding design point x
x′rJ-th of element value；
Step 7: will w expression formula in flow field be askedFlow field control equation is substituted into, the progress of stream field governing equation is discrete,
It obtains with POD base system number x ' to be askedrFor the residual error governing equation R (Φ ' of variablewx′r；X)=0, wherein
Step 8: using gauss-newton method to residual error governing equation R (Φ 'wx′r；X) it=0 is solved:
Step 8.1: residual error governing equation is projected on the test space L by one group of base Ψ；It obtains containing nwA unknown quantity
Static determinacy equation group ΨTR(Φ′wx′r；X)=0, wherein Ψ=J Φ 'w, J is Jacobian matrix；
Step 8.2: to formula
ΨTJkΦ′wpk=-ΨTRk
It is iterated solution, obtains POD base system number x 'r；Wherein k=1 ..., K are Newton iteration step, and K is determined by convergence, pk
WithRespectively kth step iteration when POD base system number increment and Jacobian matrix, αkIt is in pkStep in the direction of search
It is long,For initial value, by formulaIt obtains；
Step 8.3: according to POD base system number x 'r, obtain the flow field w under design point xrom=Φ 'wx′r；
Step 9: the CFD amendment of local flow field:
Using the residual error R of the last one iteration step in step 8 as foundation, the mesh point for selecting residual error to be greater than given threshold carries out CFD
Amendment: with wromAs first field, the mesh point for calling CFD fluid diagnosis to be greater than given threshold to residual error is solved, other nets
Lattice point flow field value remains unchanged and as solution boundary condition；Stop solving when residual error R drops to given threshold or less；
Step 10: combining the flow field under design point x that the flow field of step 9 local correction is obtained with step 8, obtain design point x
Final Flow Field Solution.
2. a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep according to claim 1, feature
It is: aerocraft flying parameter design space sample point x is obtained using Latin hypercube experimental design method in step 1i, i=
1,2,…,n。
3. a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep according to claim 1, feature
It is: using the flow field sampling solution w of each sample point in CFD fluid diagnosis obtaining step 1 in step 2i, i=1,2 ... n.
4. a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep according to claim 1, feature
Be: radial basis function r () uses gauss of distribution function in step 4:D is Euclidean distance.
5. a kind of aircraft flow field of region containing shock wave quick calculation method based on multistep according to claim 1, feature
It is: in step 9, using the residual error R of the last one iteration step in step 8 as foundation, using Domain Decomposition Method, selects residual error big
In the region that the mesh point of given threshold forms as the modified region of needs；The grid in modified region will be needed from former grid
In individually take out, with wromAs first field and boundary condition, call CFD fluid diagnosis to the grid list for needing modified region
It solely solves, stops solving when residual error R drops to given threshold or less.
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| CN106682262B (en) * | 2016-11-21 | 2019-12-20 | 中国航天空气动力技术研究院 | Numerical simulation method for obtaining aircraft flow field |
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| CN107256290B (en) * | 2017-05-19 | 2020-07-10 | 四川腾盾科技有限公司 | Method for calculating influence difference of boundary change on flow field based on residual perturbation method |
| CN108595788A (en) * | 2018-04-05 | 2018-09-28 | 西北工业大学 | A kind of flow field Accelerated Convergence Method based on mode multi grid |
| CN110826208B (en) * | 2019-10-30 | 2023-04-07 | 北京机电工程研究所 | Pneumatic numerical simulation accelerated convergence method |
| CN111339672B (en) * | 2020-03-02 | 2021-06-08 | 上海索辰信息科技股份有限公司 | Method for analyzing aerodynamic thermal simulation of shock wave at front edge of air inlet channel |
| CN111611646B (en) * | 2020-04-08 | 2024-04-12 | 南京航空航天大学 | Rapid design method for aerodynamic configuration of aircraft precursor |
| CN111859817B (en) * | 2020-05-22 | 2024-01-16 | 中国航空工业集团公司西安航空计算技术研究所 | Aircraft pneumatic model selection method based on CFD software shock wave simulation capability |
| CN111814341A (en) * | 2020-07-16 | 2020-10-23 | 西北工业大学 | Method for performing nonlinear flutter analysis of wallboard based on POD (wafer POD) order reduction method |
| CN112162957B (en) * | 2020-10-13 | 2022-05-27 | 中国空气动力研究与发展中心计算空气动力研究所 | Multi-block structure grid data compression storage method, decompression method and device |
| CN112016167B (en) * | 2020-10-22 | 2021-01-29 | 中国人民解放军国防科技大学 | Aircraft aerodynamic shape design method and system based on simulation and optimization coupling |
| CN112784508A (en) * | 2021-02-12 | 2021-05-11 | 西北工业大学 | Deep learning-based airfoil flow field rapid prediction method |
| CN113379103B (en) * | 2021-05-20 | 2022-05-13 | 中国船舶重工集团公司第七一九研究所 | Prediction method of pump equipment internal flow field based on reduced order model |
| CN114065662B (en) * | 2021-11-12 | 2022-09-02 | 西北工业大学 | Method suitable for rapidly predicting airfoil flow field with variable grid topology |
| CN117892660B (en) * | 2024-03-14 | 2024-05-28 | 中国空气动力研究与发展中心计算空气动力研究所 | Method and device for selecting reference Mach number in low-speed preprocessing |
| CN118052167B (en) * | 2024-04-16 | 2024-07-02 | 中国空气动力研究与发展中心计算空气动力研究所 | Method for constructing flow field model with multidimensional correlation response |
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