SOLUTION INTERPOLATION FOR HIGH-ORDER ACCURATE ADAPTIVE FLOW SIMULATION

Zhou Shuai; Xiao Zhoufang; Fu Lin; Wang Dingshun

doi:10.6052/0459-1879-22-060

Volume 54 Issue 6

May 2022

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Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(6): 1732-1740

Zhou Shuai, Xiao Zhoufang, Fu Lin, Wang Dingshun. Solution interpolation for high-order accurate adaptive flow simulation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1732-1740 doi: 10.6052/0459-1879-22-060

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Zhou Shuai, Xiao Zhoufang, Fu Lin, Wang Dingshun. Solution interpolation for high-order accurate adaptive flow simulation. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1732-1740 doi: 10.6052/0459-1879-22-060

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SOLUTION INTERPOLATION FOR HIGH-ORDER ACCURATE ADAPTIVE FLOW SIMULATION

doi: 10.6052/0459-1879-22-060

*.
Aero Engine Academy of China, Beijing 101300, China
†.
School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China

Received Date: 2022-01-31
Accepted Date: 2022-03-30

Available Online: 2022-03-31

Publish Date: 2022-06-18

Abstract

Abstract

Mesh adaptation and high order numerical methods are regarded as effective techniques to improve the adaptability of computational fluid dynamics (CFD) to complex problems. The combination of these two techniques requires solving a series of technical challenges, one of which is the flow field interpolation for high order numerical methods among different adaptation steps. A high-order accurate solution interpolation method is proposed for the high-order accurate adaptive flow simulation. In this method, it interpolates the numerical flow solution from the mesh in the previous iteration step into the mesh of the current iteration step, to allow the simulation to be restarted from the previous state. To realize the conservation of physical quantities in the process of flow field interpolation, the method first computes the overlapping regions of the new and old meshes and then transfers the physical quantities from the old mesh to the new mesh in the overlapping regions. To achieve high-order accuracy, the k-exact least-squares method is first used to reconstruct the numerical solution on the old mesh, and as a result, a polynomial with the required order that represents the distribution of the physical quantity is obtained over each element of the background mesh. Then Gaussian numerical integration is used to integrate the physical quantities over each element of the new mesh, which accurately transfers the physical quantities from the background mesh to each element of the new mesh. Finally, the effectiveness of the proposed algorithm is verified by a numerical example with an exact solution and an example of high-order accurate adaptive flow simulation. The results of the first example show that a smaller interpolation error exists when higher-order accurate interpolation is adopted, and the second example shows that the method in this paper can effectively shorten the iterative convergence time of high order accurate flow simulation.
- solution interpolation,
- adaptive simulation,
- high order numerical method,
- mesh adaptation,
- computational fluid dynamics

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References(33)

References

[1]	张来平, 常兴华, 赵钟等. 计算流体力学网格生成技术. 北京: 科学出版社, 2017 Zhang Laiping, Chang Xinghua, Zhao Zhong, et al. Mesh Generation Techniques in Computational Fluid Dynamics. Beijing: Science Press, 2017 (in Chinese)
[2]	Park MA, Loseille A, Krakos J, et al. Unstructured grid adaptation: status, potential impacts, and recommended investments towards CFD 2030//46th AIAA Fluid Dynamics Conference, 2016, 2016-3323
[3]	Caplan PC, Haimes R, Darmofal DL, et al. Extension of local cavity operators to 3D + t space-time mesh adaptation//AIAA Scitech 2019 Forum, 2019, 2019-1992
[4]	Caplan PC, Haimes R, Darmofal DL, et al. Four-dimensional anisotropic mesh adaptation. Computer-Aided Design, 2020, 129: 102915 doi: 10.1016/j.cad.2020.102915
[5]	Loseille A, Alauzet F, Menier V. Unique cavity-based operator and hierarchical domain partitioning for fast parallel generation of anisotropic meshes. Computer-Aided Design, 2017, 85: 53-67 doi: 10.1016/j.cad.2016.09.008
[6]	Xiao ZF, Ollivier-Gooch C, Vazquez JDZ. Anisotropic tetrahedral mesh adaptation with improved metric alignment and orthogonality. Computer-Aided Design, 2022, 143: 103136 doi: 10.1016/j.cad.2021.103136
[7]	Sharbatdar M, Ollivier-Gooch C. Mesh adaptation using C1 interpolation of the solution in an unstructured finite volume solver. International Journal for Numerical Methods in Fluids, 2018, 86(10): 637-654 doi: 10.1002/fld.4471
[8]	Coulaud O, Loseille A. Very high order anisotropic metric-based mesh adaptation in 3D. Procedia Engineering, 2016, 163: 353-365 doi: 10.1016/j.proeng.2016.11.071
[9]	Wang ZJ, Fidkowski K, Abgrall R, et al. High‐order CFD methods: current status and perspective. International Journal for Numerical Methods in Fluids, 2013, 72(8): 811-845 doi: 10.1002/fld.3767
[10]	Hoshyari S, Mirzaee E, Ollivier-Gooch C. Efficient convergence for a higher-order unstructured finite volume solver for compressible flows. AIAA Journal, 2020, 58(4): 1490-1505 doi: 10.2514/1.J058537
[11]	廖飞. 高阶精度数值方法及其在复杂流动中的应用. [博士论文]. 西安: 西北工业大学, 2018 Liao Fei. Efficient high-order high-resolution methods and the applications. [PhD Thesis]. Changsha: Northwestern Polytechnical University, 2018 (in Chinese)
[12]	Pan JH, Ren YX, Sun YT. High order sub-cell finite volume schemes for solving hyperbolic conservation laws. II: Extension to two-dimensional systems on unstructured grids. Journal of Computational Physics, 2017, 338: 165-198 doi: 10.1016/j.jcp.2017.02.052
[13]	雷国东, 李万爱, 任玉新. 求解可压缩流的高精度非结构网格WENO有限体积法. 计算物理, 2011, 28(5): 633-640 (Lei Guodong, Li Wanai, Ren Yuxin. A high-order unstructured-grid WENO FVM for compressible flow computation. Chinese Journal of Computational Physics, 2011, 28(5): 633-640 (in Chinese) Lei Guodong, Li Wanai, Ren Yuxin, A high-order unstructured-grid WENO FVM for compressible flow computation. Chinese Journal of Computational Physics, 2011, 28(5): 633-640 (in Chinese))
[14]	Xu Z, Cambier L, Alonso JJ, et al. Towards a scalable hierarchical high-order CFD solver//AIAA Scitech 2021 Forum, 2021, 2021-0494
[15]	Alauzet F, Mehrenberger M. P1-conservative solution interpolation on unstructured triangular meshes. International Journal for Numerical Methods in Engineering, 2010, 84(13): 1552-1588 doi: 10.1002/nme.2951
[16]	王瑞利. 散乱物理量逼近的插值重映算法. 计算物理, 2005, 22(4): 299-305 (Wang Ruili. An interpolated remapping algorithm for scattered physics quantities. Chinese Journal of Computational Physics, 2005, 22(4): 299-305 (in Chinese) doi: 10.3969/j.issn.1001-246X.2005.04.003 Wang Ruili. An interpolated remapping algorithm for scattered physics quantities. Chinese Journal of Computational Physics, 2005, 22(04): 299-305 (in Chinese)) doi: 10.3969/j.issn.1001-246X.2005.04.003
[17]	王永健, 赵宁. 一类基于 ENO 插值的守恒重映算法. 计算物理, 2004, 21(4): 329-334 (Wang Yongjian, Zhao Ning. A kind of rezoning(remapping) algorithms based on ENO Interpolation. Chinese Journal of Computational Physics, 2004, 21(4): 329-334 (in Chinese) doi: 10.3969/j.issn.1001-246X.2004.04.008 Wang Yongjian, Zhao Ning. A kind of rezoning(remapping) algorithms based on ENO Interpolation. Chinese Journal of Computational Physics, 2004, 21(4): 329-334 (in Chinese)) doi: 10.3969/j.issn.1001-246X.2004.04.008
[18]	赵小杰, 赵宁, 王东红. 一类基于RBF插值的守恒重映算法. 计算物理, 2012, 29(1): 10-16 (Zhao Xiaojie, Zhao Ning, Wang Donghong. A kind of conservative remapping algorithms based on RBF interpolations. Chinese Journal of Computational Physics, 2012, 29(1): 10-16 (in Chinese) doi: 10.3969/j.issn.1001-246X.2012.01.002 Zhao Xiaojie, Zhao Ning, Wang Donghong. A kind of conservative remapping algorithms based on RBF interpolations. Chinese Journal of Computational Physics, 2012, 29(1): 10-16 (in Chinese)) doi: 10.3969/j.issn.1001-246X.2012.01.002
[19]	徐喜华, 刘娜, 陈艺冰. 非结构多面体二阶局部保界全局重映算法. 计算物理, 2018, 35(1): 22-28 (Xu Xihua, Liu Na, Chen Yibing. Second-order local-bound-preserving conservative remapping on unstructured polyhedral meshes. Chinese Journal of Computational Physics, 2018, 35(1): 22-28 (in Chinese) Xu Xihua, Liu Na, ChenYibing. Second-order local-bound-preserving conservative remapping on unstructured polyhedral meshes. Chinese Journal of Computational Physics, 2018, 35(1): 22-28 (in Chinese))
[20]	Farrell PE, Piggott MD, Pain CC, et al. Conservative interpolation between unstructured meshes via supermesh construction. Computer Methods in Applied Mechanics and Engineering, 2009, 198(33-36): 2632-2642 doi: 10.1016/j.cma.2009.03.004
[21]	Slattery SR. Mesh-free data transfer algorithms for partitioned multiphysics problems: conservation, accuracy, and parallelism. Journal of Computational Physics, 2016, 307: 164-188 doi: 10.1016/j.jcp.2015.11.055
[22]	Alauzet F. A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes. Computer Methods in Applied Mechanics and Engineering, 2016, 299: 116-142 doi: 10.1016/j.cma.2015.10.012
[23]	Cheng J, Shu CW. A high order accurate conservative remapping method on staggered meshes. Applied Numerical Mathematics, 2008, 58(7): 1042-1060 doi: 10.1016/j.apnum.2007.04.015
[24]	Lei N, Cheng J, Shu CW. A high order positivity-preserving conservative WENO remapping method on 2D quadrilateral meshes. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113497
[25]	Zhang M, Huang WZ, Qiu JX. High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer. SIAM Journal on Scientific Computing, 2020, 42(5): A3109-A3135 doi: 10.1137/19M1297907
[26]	Ollivier-Gooch C, Nejat A, Michalak K. Obtaining and verifying high-order unstructured finite volume solutions to the Euler equations. AIAA Journal, 2009, 47(9): 2105-2120 doi: 10.2514/1.40585
[27]	Lo SH, Wang WX. A fast robust algorithm for the intersection of triangulated surfaces. Engineering with Computers. 2004, 20(1): 11-21
[28]	Campen M, Kobbelt L. Exact and robust (self-) intersections for polygonal meshes//Computer Graphics Forum, 2010: 397-406
[29]	McLaurin D, Marcum D, Remotigue M, et al. Repairing unstructured triangular mesh intersections. International Journal for Numerical Methods in Engineering. 2013, 93(3): 266-275
[30]	Stroud AH, Secrest D. Gaussian Quadrature Formulas. Englewood Cliffs: Prentice-Hall, 1966
[31]	Pagnutti D, Ollivier-Gooch C. A generalized framework for high order anisotropic mesh adaptation. Computers & Structures, 2009, 87(11-12): 670-679
[32]	Xiao ZF, Ollivier-Gooch C. Smooth gradation of anisotropic meshes using log-euclidean metrics. AIAA Journal, 2021, 59(10): 4105-4122 doi: 10.2514/1.J059864
[33]	Malik S, Ollivier Gooch CF. Mesh adaptation for wakes via surface insertion//AIAA Scitech 2019 Forum, 2019, 2019-1996