CN108197367B - High-precision intermittent Galerkin artificial viscous shock wave capturing method - Google Patents
High-precision intermittent Galerkin artificial viscous shock wave capturing method Download PDFInfo
- Publication number
- CN108197367B CN108197367B CN201711443613.2A CN201711443613A CN108197367B CN 108197367 B CN108197367 B CN 108197367B CN 201711443613 A CN201711443613 A CN 201711443613A CN 108197367 B CN108197367 B CN 108197367B
- Authority
- CN
- China
- Prior art keywords
- equation
- cell
- precision
- artificial
- artificial viscosity
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a high-precision discontinuous Galerkin artificial viscosity shock wave capturing method based on flow field flux step.A non-structural grid is adopted to subdivide a calculation area, a control equation adopts an Euler equation, a DG high-precision frame represented by a basis function, a test function and Gauss integral points is established, a new artificial viscosity item is constructed in the equation on the basis of the step of a conservative variable on a unit interface, the convection item of the equation is discretely solved in an HLL format, and under the condition of effectively capturing shock waves, robustness and calculation precision are ensured; according to the method, even under the condition that shock wave capture is not carried out, the flux at the cell interface is also an intermediate variable necessary for equation solution, the flux step at the flow field cell interface is selected to construct artificial viscosity, and compared with other methods, the method can reduce the calculation amount, so that the calculation time is saved.
Description
Technical Field
The invention relates to a computational fluid mechanics technology basin, in particular to a high-precision intermittent Galerkin artificial viscous shock wave capturing method based on flow field flux step.
Background
The high-precision DG method has the excellent characteristics in the aspects of numerical dissipation and dispersion at present, is ideally very suitable for solving the complex multi-scale problem in fluid calculation, and achieves certain achievements in the calculation of low-speed incompressible fluid and is widely applied. However, when the high-precision DG method is applied to calculation of compressible fluid, shock waves can be generated in a flow field, according to the Godunov principle, the Gibbs phenomenon can be generated near shock wave discontinuity by the high-precision DG method, so that non-physical understanding is generated, and calculation interruption is caused. Shock capture has become a major bottleneck hindering the development of high-precision DG methods in compressible fluid computing. At present, high-precision DG shock wave capturing methods are not mature enough, and the conventional shock wave capturing method mainly comprises a limiter and reconstruction. The methods capture the shock waves by adopting a post-processing mode, uncontrollable nonlinear terms can be introduced in the whole solving process when the modes are adopted, and due to the introduction of the nonlinear terms, the situation of mismatching between the physical process and a control equation can exist, so that the problems of serious degradation, poor convergence, poor robustness, easy occurrence of non-physical oscillation, insufficient 'sharpness' of shock wave capture and the like of a shock wave area can be directly caused.
Disclosure of Invention
The invention aims to provide a high-precision intermittent Galerkin artificial viscous shock wave capturing method, which constructs a new artificial viscous shock wave capturing method by adopting flux steps on a unit interface in a flow field according to the characteristics and dimension analysis principle of shock waves and is mainly used for solving the problems of poor convergence, poor robustness, easy occurrence of non-physical shock, insufficient 'sharpness' of shock wave capturing and the like in the process of shock wave capturing of a high-precision DG method.
In order to achieve the purpose, the invention adopts the following technical scheme:
a high-precision intermittent Galerkin artificial viscous shock wave capturing method based on flow field flux steps comprises the following steps:
the method comprises the following steps: establishing a high-precision DG framework which comprises information such as grid subdivision, an Euler control equation, basis functions in a finite element method, test functions, Gauss integral points and the like;
step two: constructing an artificial viscosity coefficient within the cell based on the flux step at the cell interface;
step three: and substituting the artificial viscosity coefficient into an Euler control equation, and solving to obtain a simulation calculation result.
The invention adopts an unstructured grid to subdivide a calculation area, adopts a control equation of an Euler equation, and establishes a DG high-precision frame represented by a basis function, a test function and Gauss integral points. Meanwhile, a new artificial viscosity term is constructed on the basis of the step of the conservation variable on the unit interface in the equation, and the convection term of the equation is discretely solved by adopting an HLL format. Under the condition of effectively capturing shock waves, robustness and calculation accuracy are guaranteed.
Compared with the prior art, the invention is characterized in that:
1. even in the case of not carrying out shock wave capture, the flux at the unit interface is an intermediate variable necessary for equation solution, and the flux step at the flow field unit interface is selected to construct artificial viscosity, so that the calculation amount can be reduced compared with other methods, and the calculation time can be saved.
2. The method adopts a flux step artificial viscosity method to capture shock waves, the pressure distribution curve is sharper near the shock waves, and the convergence is superior to other methods.
Drawings
The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a one-dimensional sod problem computed using the method of the present invention;
FIG. 3 is a comparison of the convergence curves calculated for the NACA0012 airfoil using the method of the present invention with other methods.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
The invention discloses a high-precision intermittent Galerkin artificial viscous shock wave capturing method based on flow field flux step, which comprises three parts as shown in figure 1.
A first part: and establishing a high-precision DG framework, including calculation and storage of information such as grid subdivision, Euler control equations, basis functions in finite element methods, test functions, Gauss integral points and the like. The method comprises the following steps:
Step 102, constructing Euler equation under differential form
Wherein U represents the conservation in the flow field, U is a vector, and U ═ p, ρ U, ρ v, ρ w, ρ E)T，
Representing the partial derivative of the conservative quantity with respect to time t, FcWhich represents a conserved flux, is,
representing the divergence of the conserved flux.
103, selecting Taylor base as a basis function and a test function, wherein the conservation quantity in the flow field is expressed by linear combination of the basis functions
And calculating volume fraction Gauss integral points and surface integral Gauss integral points under different types of grids, and storing the volume fraction Gauss integral points and the surface integral Gauss integral points in an internal memory for later use.
104, substituting the linear combination of the conservation quantities into an Euler control equation (1), integrating the equation, simultaneously multiplying the two sides of the equation by a basis function phi, and obtaining a DG solution equation under a weak situation by utilizing a Green Gauss formula
Wherein, M ═ n ^ nΩφiφjRepresenting the mass matrix, u represents the coefficients used when the conservation variables are linearly combined with basis functions, also called degrees of freedom,
representing the derivative of the degree of freedom with respect to time.
In order to be a boundary surface of the cell,
in the direction of the outer normal of the cell boundary surface,
representing the gradient of the basis function.
A second part: constructing an artificial viscosity coefficient within the cell based on the flux step at the cell interface, comprising the steps of:
step 201, selecting a Laplace artificial viscosity model, substituting the Laplace artificial viscosity model into a formula (1), and repeating the steps 103 and 104 to obtain a DG solving equation containing an artificial viscosity term
Wherein epsilon is an artificial viscosity coefficient, determines the value of artificial viscosity in the unit,
representing the gradient of the degree of freedom.
Step 202, reconstructing the artificial viscosity coefficient ε, selecting a logical connection at the cell interfaceStep of magnitude
(
And
representing flux values on both the left and right sides of the cell interface) and the average of the conservative variables
(
And
representing the values of the conservation variables on the left and right sides of the cell interface) are linearly combined to construct a middle step U at the interfacejump
Step 203, the intermediate step quantity U obtained in step 202jumpIntegrating at the interface of the cell, and dividing the integral quantity by the total area S of the cell to obtain the distribution U of the step quantity in the cellcell
Step 204, utilizing the step distribution U in the unit bodycellAnd pressure gradient at the cell core
Empirical parameter C∈And multiplying the reference scale h of the local grid cell by the reference scale h of the local grid cell, and dividing the multiplied product by the pressure p at the center of the cell body to construct an artificial viscosity coefficient epsilon in the cell
And a third part: substituting the artificial viscosity coefficient into a control equation, and solving to obtain a simulation calculation result;
and step 301, substituting the artificial viscosity coefficient epsilon in the cell obtained in the step 204 into a DG solution equation (3) containing an artificial viscosity term.
And 302, dispersing a DG solution equation, and solving a control equation through iterative calculation to obtain a simulated pneumatic result and a flow field.
As shown in FIG. 2, for the one-dimensional sod problem calculated by the method of the present invention, it can be seen that the curve distribution is "sharper" near the shock, and for the shock region, the pressure or density curve should theoretically be a vertical line, and if the calculation result is "sharper", the result is closer to the theoretical value, and it is apparent from FIG. 2 that the new method is superior to other methods in "sharpness" degree, and the result is closer to the theoretical value. For the calculation results of the new method in fig. 2, fig. 3 shows the calculated convergence curve of the NACA0012 airfoil profile using the method of the present invention compared with other methods, and it is obvious that the calculated convergence time of the method is significantly shorter than that of other methods.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.
Claims (3)
1. A high-precision intermittent Galerkin artificial viscous shock wave capturing method based on flow field flux step is characterized by comprising the following steps:
the method comprises the following steps: establishing a high-precision DG framework which comprises information of grid subdivision, an Euler control equation, a basis function in a finite element method, a test function and Gauss integral points;
in the first step, establishing a high-precision DG frame comprises the following steps:
step 101: adopting non-structural grids to carry out grid subdivision on the calculation area;
step 102: constructing an Euler equation in a differential form;
step 103: selecting a Taylor base as a basis function and a test function, expressing the conservative quantity in a flow field by adopting the linear combination of the basis functions, calculating volume fraction Gauss integral points and surface fraction Gauss integral points under different types of grids, and storing the points in an internal memory for later use;
step 104: substituting linear combination of conservative quantities into an Euler control equation under a differential form, integrating the equation, simultaneously multiplying two sides of the equation by a basis function, and obtaining a DG solution equation under a weak situation by utilizing a Green Gaussian formula;
step two: constructing an artificial viscosity coefficient within the cell based on the flux step at the cell interface;
in said second step, constructing an artificial viscosity coefficient within the cell based on the flux step at the cell interface comprises the steps of:
step 201: selecting a Laplace artificial viscosity model, substituting into a Euler equation under a differential form, and repeating the third step and the fourth step of establishing a high-precision DG framework to obtain a DG solution equation containing an artificial viscosity term;
step 202: reconstructing the artificial viscosity coefficient, selecting the step of the conservation variable at the interface of the unit and the average value of the conservation variable to carry out linear combination, and constructing the middle step at the interface;
step 203: integrating the intermediate step quantity obtained in the step 202 at the interface of the cell, and then dividing the integrated quantity by the total area of the cell to obtain the distribution of the step quantity in the cell body;
step 204: multiplying the step distribution in the cell body, the pressure gradient at the center of the cell body, the empirical parameters and the reference scale of the local grid cell, and dividing by the pressure at the center of the cell body to construct an artificial viscosity coefficient in the cell;
step three: and substituting the artificial viscosity coefficient into an Euler control equation, and solving to obtain a simulation calculation result.
2. The method for capturing high-precision interrupted Galerkin artificial viscous shock waves based on flow field flux steps as claimed in claim 1, wherein in the step 101, for a two-dimensional computation domain, the subdivided mesh types comprise triangles and quadrilaterals, and for a three-dimensional computation domain, the subdivided mesh types comprise tetrahedrons, hexahedrons, triangular prisms and pyramid outlines.
3. The method for capturing the high-precision intermittent Galerkin artificial viscous shock wave based on the flow field flux step as claimed in claim 1, wherein the artificial viscosity coefficient calculated in step 204 is substituted into a DG solution equation containing an artificial viscosity term, the DG solution equation is discretized, and a control equation is solved through iterative computation to obtain a simulated pneumatic result and a flow field.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711443613.2A CN108197367B (en) | 2017-12-27 | 2017-12-27 | High-precision intermittent Galerkin artificial viscous shock wave capturing method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711443613.2A CN108197367B (en) | 2017-12-27 | 2017-12-27 | High-precision intermittent Galerkin artificial viscous shock wave capturing method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108197367A CN108197367A (en) | 2018-06-22 |
| CN108197367B true CN108197367B (en) | 2021-07-27 |
Family
ID=62584442
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201711443613.2A Active CN108197367B (en) | 2017-12-27 | 2017-12-27 | High-precision intermittent Galerkin artificial viscous shock wave capturing method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108197367B (en) |
Families Citing this family (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111159956B (en) * | 2019-12-10 | 2021-10-26 | 北京航空航天大学 | Feature-based flow field discontinuity capturing method |
| CN112665820B (en) * | 2021-03-15 | 2021-06-04 | 中国空气动力研究与发展中心计算空气动力研究所 | R-type grid self-adaptive moving method and device based on variable difference and relative displacement |
| CN113591417B (en) * | 2021-08-11 | 2023-02-24 | 中国空气动力研究与发展中心计算空气动力研究所 | Viscous item processing method applied to high-precision Anzelia galamurensis fluid simulation |
| CN113742967B (en) * | 2021-08-27 | 2023-10-31 | 北京航空航天大学 | Intermittent finite element artificial viscous shock wave processing method based on strong residual error |
| CN113656920B (en) * | 2021-10-20 | 2021-12-21 | 中国空气动力研究与发展中心计算空气动力研究所 | Missile rudder surface hinge moment design method capable of reducing power redundancy of steering engine |
| CN114091376B (en) * | 2022-01-21 | 2022-04-12 | 中国空气动力研究与发展中心计算空气动力研究所 | High-precision reconstruction correction shock wave capturing method based on subunit weighting format |
| CN114638173B (en) * | 2022-01-25 | 2023-06-02 | 中国空气动力研究与发展中心计算空气动力研究所 | Space discrete method for capturing high-order nonlinear shock waves |
| CN114611421B (en) * | 2022-02-16 | 2023-07-07 | 上海机电工程研究所 | Artificial viscosity method and system based on modal attenuation |
| CN115238397B (en) * | 2022-09-15 | 2022-12-02 | 中国人民解放军国防科技大学 | Method and device for calculating thermal environment of hypersonic aircraft and computer equipment |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002110807A (en) * | 2000-09-29 | 2002-04-12 | Fujitsu Ltd | Allotment method of timing limitation, and allotment device |
| CN1764917A (en) * | 2003-02-05 | 2006-04-26 | 莫尔德弗洛爱尔兰有限公司 | Apparatus and methods for performing process simulation using a hybrid model |
| CN102682146A (en) * | 2011-11-30 | 2012-09-19 | 天津空中代码工程应用软件开发有限公司 | Method for simulating numerical value of compressible vortex flow field |
| CN104036095A (en) * | 2014-06-27 | 2014-09-10 | 北京航空航天大学 | Regional-decomposition based high-precision coupling fast-calculation method for complex-shape flow field |
| CN104298823A (en) * | 2014-10-09 | 2015-01-21 | 中国空气动力研究与发展中心高速空气动力研究所 | Analysis method and system of high- and low-temperature balances |
| CN105893693A (en) * | 2016-04-21 | 2016-08-24 | 北京航空航天大学 | Compressible turbulence direct numerical simulation method based on compact type high resolution hybrid format |
| CN106682262A (en) * | 2016-11-21 | 2017-05-17 | 中国航天空气动力技术研究院 | Numerical simulation method for obtaining aircraft flow fields |
-
2017
- 2017-12-27 CN CN201711443613.2A patent/CN108197367B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002110807A (en) * | 2000-09-29 | 2002-04-12 | Fujitsu Ltd | Allotment method of timing limitation, and allotment device |
| CN1764917A (en) * | 2003-02-05 | 2006-04-26 | 莫尔德弗洛爱尔兰有限公司 | Apparatus and methods for performing process simulation using a hybrid model |
| CN102682146A (en) * | 2011-11-30 | 2012-09-19 | 天津空中代码工程应用软件开发有限公司 | Method for simulating numerical value of compressible vortex flow field |
| CN104036095A (en) * | 2014-06-27 | 2014-09-10 | 北京航空航天大学 | Regional-decomposition based high-precision coupling fast-calculation method for complex-shape flow field |
| CN104298823A (en) * | 2014-10-09 | 2015-01-21 | 中国空气动力研究与发展中心高速空气动力研究所 | Analysis method and system of high- and low-temperature balances |
| CN105893693A (en) * | 2016-04-21 | 2016-08-24 | 北京航空航天大学 | Compressible turbulence direct numerical simulation method based on compact type high resolution hybrid format |
| CN106682262A (en) * | 2016-11-21 | 2017-05-17 | 中国航天空气动力技术研究院 | Numerical simulation method for obtaining aircraft flow fields |
Non-Patent Citations (3)
| Title |
|---|
| A simple shock‐capturing technique for high‐order discontinuous Galerkin methods;Huerta A 第;《International Journal for Numerical Methods in Fluids》;20120830;1614–1632 * |
| 基于人工粘性的间断Galerkin有限元方法;于剑，阎超;《空气动力学学报》;20130630;371-375 * |
| 超声速不同介质横向喷流数值模拟;赵辉;《中国优秀硕士学位论文全文数据库（工程科技Ⅱ辑）》;20150515;C032-15 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108197367A (en) | 2018-06-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108197367B (en) | High-precision intermittent Galerkin artificial viscous shock wave capturing method | |
| CN108197072B (en) | High-precision intermittent Galerkin artificial viscous shock wave capturing method based on weighted conservative variable step | |
| Bandringa | Immersed boundary methods | |
| Hou et al. | A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment | |
| Hou et al. | A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography | |
| Paluszny et al. | Numerical fracture growth modeling using smooth surface geometric deformation | |
| Kazolea et al. | An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations | |
| Dettmer et al. | A stabilised immersed boundary method on hierarchical b-spline grids | |
| CN108153984B (en) | High-precision Galois gold artificial viscous shock wave capturing method based on flow field density step | |
| de Jesus et al. | A 3D front-tracking approach for simulation of a two-phase fluid with insoluble surfactant | |
| Rashid et al. | A three‐dimensional finite element method with arbitrary polyhedral elements | |
| Fogg et al. | Automatic generation of multiblock decompositions of surfaces | |
| Lee et al. | Simple and efficient solution of the shallow water equations with source terms | |
| Lin et al. | Quality guaranteed all-hex mesh generation by a constrained volume iterative fitting algorithm | |
| Wang et al. | Feature-sensitive tetrahedral mesh generation with guaranteed quality | |
| CN116629079B (en) | Method and device for constructing mixed finite element space and solving linear elastic mechanical problem | |
| Sohn et al. | A novel scheme to generate meshes with hexahedral elements and poly-pyramid elements: The carving technique | |
| Meßmer et al. | Efficient CAD-integrated isogeometric analysis of trimmed solids | |
| Tang et al. | An efficient adaptive analysis procedure using the edge-based smoothed point interpolation method (ES-PIM) for 2D and 3D problems | |
| Liu et al. | Error-bounded edge-based remeshing of high-order tetrahedral meshes | |
| Esser et al. | An extended finite element method applied to levitated droplet problems | |
| Premasuthan et al. | Computation of flows with shocks using spectral difference scheme with artificial viscosity | |
| Balu et al. | Direct immersogeometric fluid flow and heat transfer analysis of objects represented by point clouds | |
| Jankuhn et al. | Higher order trace finite element methods for the surface Stokes equation | |
| Zhang et al. | A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| CB03 | Change of inventor or designer information |
Inventor after: Zhao Hui Inventor after: Ma Mingsheng Inventor after: Wu Xiaojun Inventor after: Zhang Yaobing Inventor after: Chen Jiangtao Inventor after: Liu Wei Inventor after: Zhang Peihong Inventor after: Gong Xiaoquan Inventor after: Yang Yueyue Inventor before: Zhao Hui Inventor before: Liu Wei Inventor before: Chen Jiangtao Inventor before: Ma Mingsheng |
|
| CB03 | Change of inventor or designer information | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |