ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Spatial discretization algorithm for cell-centered finite volume method based on face gradient reconstruction
Received date: 2023-02-10
Revised date: 2023-03-03
Accepted date: 2023-03-27
Online published: 2023-04-07
Supported by
National Natural Science Foundation of China(11872144)
The gradient reconstruction process determines the spatial discretization accuracy and robustness of the finite volume method. A novel gradient reconstruction method is proposed for the cell-centered finite volume method. Based on the weighted least squares principle， this method calculates the face-centered variables and the gradient of these variables and then solves the cell-centered gradient using either central difference or arithmetic averaging methods for different grid types. Finally， a new boundary constraint algorithm adapted to the new gradient reconstruction method is developed by combining boundary conditions with the gradient reconstruction process. A grid convergence study using an exact test function shows that the new method can achieve the linear reconstruction of the full-field gradient under smooth solution conditions. A series of inviscid and viscous flow cases show that， compared with the previous method， this method can effectively reduce the numerical dissipation in the near boundary region and improve the computational accuracy with better robustness under the large aspect ratio triangular grid.
Yanxin WEI , Jun LIU . Spatial discretization algorithm for cell-centered finite volume method based on face gradient reconstruction[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(1) : 128541 -128541 . DOI: 10.7527/S1000-6893.2023.28541
| 1 | ABGRALL R. On essentially non-oscillatory schemes on unstructured meshes： Analysis and implementation［J］. Journal of Computational Physics， 1994， 114（1）： 45-58. |
| 2 | HU C Q， SHU C W. Weighted essentially non-oscillatory schemes on triangular meshes［J］. Journal of Computational Physics， 1999， 150（1）： 97-127. |
| 3 | DUMBSER M， K?SER M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems［J］. Journal of Computational Physics， 2007， 221（2）： 693-723. |
| 4 | BARTH T， FREDERICKSON P. Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction∥Proceedings of the 28th Aerospace Science Meeting. Reston： AIAA， 1990. |
| 5 | BARTH T. Recent developments in high order K-exact reconstruction on unstructured meshes［C］∥ Proceedings of the 31st Aerospace Sciences Meeting. Reston： AIAA， 1993. |
| 6 | WANG Q A， REN Y X， PAN J H， et al. Compact high order finite volume method on unstructured grids III： Variational reconstruction［J］. Journal of Computational Physics， 2017， 337： 1-26. |
| 7 | 任玉新， 王乾， 潘建华， 等. 构建非结构网格高精度有限体积方法的新途径［J］. 航空学报， 2021， 42（9）： 625783. |
| REN Y X， WANG Q， PAN J H， et al. Novel approaches to design of high order finite volume schemes on unstructured grids［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（9）： 625783 （in Chinese）. | |
| 8 | EKATERINARIS J A. High-order accurate， low numerical diffusion methods for aerodynamics［J］. Progress in Aerospace Sciences， 2005， 41（3-4）： 192-300. |
| 9 | WANG Z J. High-order methods for the Euler and Navier–stokes equations on unstructured grids［J］. Progress in Aerospace Sciences， 2007， 43（1-3）： 1-41. |
| 10 | ANTONIADIS A F， TSOUTSANIS P， DRIKAKIS D. Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations［J］. Computers & Fluids， 2017， 146： 86-104. |
| 11 | 陈泽栋. 针对格心型有限体积法的基于格点的变量/梯度重构算法［D］. 大连： 大连理工大学， 2022. |
| CHEN Z D. Variable/gradient reconstruction algorithm based on lattice points for lattice-centered finite volume method［D］.Dalian： Dalian University of Technology， 2022 （in Chinese）. | |
| 12 | BARTH T. A 3-D upwind Euler solver for unstructured meshes［C］∥Proceedings of the 10th Computational Fluid Dynamics Conference. Reston： AIAA， 1991. |
| 13 | WEI Y X， ZHANG F， LIU J， et al. A constrained boundary gradient reconstruction method for unstructured finite volume discretization of the Euler equations［J］. Computers & Fluids， 2023， 252： 105774. |
| 14 | THOMAS J L. Accuracy of gradient reconstruction on grids with high aspect ratio： 2008-12［R］. Hampton： National Institute of Aerospace， 2013. |
| 15 | DISKIN B， THOMAS J L. Comparison of node-centered and cell-centered unstructured finite-volume discretizations： Inviscid fluxes［J］. AIAA Journal， 2011， 49（4）： 836-854. |
| 16 | DISKIN B， THOMAS J L， NIELSEN E J， et al. Comparison of node-centered and cell-centered unstructured finite-volume discretizations： Viscous fluxes［J］. AIAA Journal， 2010， 48（7）： 1326-1338. |
| 17 | CHEN Z D， ZHANG F， LIU J， et al. A vertex-based reconstruction for cell-centered finite-volume discretization on unstructured grids［J］. Journal of Computational Physics， 2022， 451： 110827. |
| 18 | 蒋跃文， 叶正寅. 适用于任意网格拓扑和质量的格心有限体积法［J］. 力学学报， 2010， 42（5）： 830-837. |
| JIANG Y W， YE Z Y. A cell-centered finite volume method for arbitrary grid type［J］. Chinese Journal of Theoretical and Applied Mechanics， 2010， 42（5）： 830-837 （in Chinese）. | |
| 19 | JAMESON A， SCHMIDT W， TURKEL E. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes［C］∥14th Fluid and Plasma Dynamics Conference. Reston： AIAA， 1981. |
| 20 | CHEN Z D， ZHANG F， LIU J， et al. An iterative near-boundary reconstruction strategy for unstructured finite volume method［J］. Journal of Computational Physics， 2020， 418： 109621. |
| 21 | WANG N H， LI M， MA R， et al. Accuracy analysis of gradient reconstruction on isotropic unstructured meshes and its effects on inviscid flow simulation［J］. Advances in Aerodynamics， 2019， 1（1）： 1-31. |
| 22 | BLAZEK J. Introduction［M］∥Computational Fluid Dynamics： Principles and Applications. Amsterdam： Elsevier， 2005： 1-4. |
| 23 | RAUWOENS P， VIERENDEELS J， MERCI B. A solution for the odd–even decoupling problem in pressure-correction algorithms for variable density flows［J］. Journal of Computational Physics， 2007， 227（1）： 79-99. |
| 24 | JALALI A， SHARBATDAR M， OLLIVIER-GOOCH C. Accuracy analysis of unstructured finite volume discretization schemes for diffusive fluxes［J］. Computers and Fluids， 2014， 101： 220-232. |
| 25 | 王年华， 李明， 张来平. 非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进［J］. 力学学报， 2018， 50（3）： 527-537. |
| WANG N H， LI M， ZHANG L P. Accuracy analysis and improvement of viscous flux schemes in unstructured second-order finite-volume discretization［J］. Chinese Journal of Theoretical and Applied Mechanics， 2018， 50（3）： 527-537 （in Chinese）. | |
| 26 | 肖艺， 明平剑. 改进最小二乘法的非结构网格梯度重构算法［J］. 哈尔滨工程大学学报， 2020， 41（12）： 1819-1826. |
| XIAO Y， MING P J. Gradient reconstruction of unstructured meshes based on improved least-squares method［J］. Journal of Harbin Engineering University， 2020， 41（12）： 1819-1826 （in Chinese）. | |
| 27 | HASELBACHER A. On constrained reconstruction operators［C］∥44th AIAA Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 2006. |
| 28 | 康忠良， 闫超. 适用于混合网格的约束最小二乘重构方法［J］. 航空学报， 2012， 33（9）： 1598-1605. |
| KANG Z L， YAN C. Constrained least-squares reconstruction method for mixed grids［J］. Acta Aeronautica et Astronautica Sinica， 2012， 33（9）： 1598-1605 （in Chinese）. | |
| 29 | 陈浩， 华如豪， 袁先旭， 等. 基于自适应笛卡尔网格的飞翼布局流动模拟［J］. 航空学报， 2022， 43（8）： 125674. |
| CHEN H， HUA R H， YUAN X X， et al. Simulation of flow around fly-wing configuration based on adaptive Cartesian grid［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（8）： 125674 （in Chinese）. | |
| 30 | DADONEL A， GROSSMAN B. Surface boundary conditions for the numerical solution of the Euler equations in three dimensions［J］. AIAA Journal， 1993， 32（2）： 285-293. |
| 31 | MENGALDO G， DE GRAZIA D， WITHERDEN F， et al. A guide to the implementation of boundary conditions in compact high-order methods for compressible aerodynamics［C］∥ Proceedings of the 7th AIAA Theoretical Fluid Mechanics Conference. Reston： AIAA， 2014. |
| 32 | VISBAL M. Evaluation of an implicit Navier-Stokes solver for some unsteady separated flows［C］∥ Proceedings of the 4th Joint Fluid Mechanics， Plasma Dynamics and Lasers Conference. Reston： AIAA， 1986. |
| 33 | COLLIS S S. Discontinuous Galerkin methods for turbulence simulation［C］∥Center for Turbulence Research Proceedings of the Summer Program，2002. |
/
| 〈 |
|
〉 |
CJA