A cell-centered discontinuous Galerkin finite element MMALE method

QING Fang; YU Xijun; ZHAO Xiaolong; ZOU Shijun; JIA Zupeng

doi:10.7638/kqdlxxb-2019.0074

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

A cell-centered discontinuous Galerkin finite element MMALE method

更新时间：2026-05-28

- A cell-centered discontinuous Galerkin finite element MMALE method
- Vol. 39, Issue 1, Pages: 25-36(2021)
- 作者机构：
  
  1. 北京应用物理与计算数学研究所, 计算物理实验室,北京,100088
  2. 中国工程物理研究院研究生院,北京,100088
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2019.0074
  CLC： O241.82
- Published：2021
- 稿件说明：
移动端阅览
卿芳, 蔚喜军, 赵晓龙, 邹世俊, 贾祖朋. 一种中心型间断有限元MMALE方法[J]. 空气动力学学报, 2021, 39(1): 25-36.

QING Fang, YU Xijun, ZHAO Xiaolong, et al. A cell-centered discontinuous Galerkin finite element MMALE method[J]. 2021, 39(1): 25-36.
卿芳, 蔚喜军, 赵晓龙, 邹世俊, 贾祖朋. 一种中心型间断有限元MMALE方法[J]. 空气动力学学报, 2021, 39(1): 25-36. DOI： 10.7638/kqdlxxb-2019.0074.

QING Fang, YU Xijun, ZHAO Xiaolong, et al. A cell-centered discontinuous Galerkin finite element MMALE method[J]. 2021, 39(1): 25-36. DOI： 10.7638/kqdlxxb-2019.0074.

摘要

针对多介质可压缩流体动力学问题，提出了一种单元中心型二维MMALE（Multi-Material Arbitrary Lagrangian-Eulerian）方法。在拉氏步，流体力学方程组采用中心型间断有限元方法求解。对于混合网格，采用Tipton压力松弛模型更新物理量，用等参坐标法更新物质中心点坐标。界面重构采用一种健壮的MOF（Moment of Fluid）方法。在重映步提出了基于多边形相交的二阶积分守恒重映方法。该方法分为四个部分：多项式重构、多边形相交、积分和后验校正。多边形相交使用“剪裁投影”算法，显著降低了多边形相交算法的复杂度。后验校正是基于MOOD（Multi-dimensional Optimal Order Detection）限制策略，并做了一些改动以适应多介质的计算。数值算例表明，该方法具有二阶的精度和较好的鲁棒性。

Abstract

A 2D cell-centered multi-material arbitrary Lagrangian-Eulerian method is presented for compressible multi-material fluid dynamics. In the Lagrangian phase

a cell-centered discontinuous Galerkin method is used to solve the hydrodynamic equations. To simplify the discrete form of these equations

an appropriate basis function with zero material derivative is selected. For mixed cells

the Tipton pressure relaxation model and the isoparametric coordinate method are used respectively to update the physical quantity and the centroids of materials. In addition

a robust MOF method is used for interface reconstruction. In the remapping phase

a second-order integral conservative remapping method is proposed. This method is based on polygon intersection and can be divided into four parts

i.e

the polynomial reconstruction

the polygon intersection

the integration

and a posteriori correction. Specifically

the polygon intersection is equipped with a "clipping and projecting" algorithm. And the posteriori correction is based on Multi-dimensional Optimal Order Detection restriction strategy with some modifications to facilitate the multi-material calculation. This correction is employed to detect problematic cells and further suppress non-physical numerical oscillations in these cells. Numerical examples show that the proposed method is of second-order accuracy and has a good robustness.

关键词

Keywords

references

HIRT C W, AMSDEN A A, COOK J L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics, 1974, 14(3): 227-253.

BENSON D J. An efficient, accurate, simple ALE method for nonlinear finite element programs[J]. Computer Methods in Applied Mechanics and Engineering, 1989, 72(3): 305-350.

BENSON D J. Computational methods in Lagrangian and Eulerian hydrocodes[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 99: 235-394.

MARGOLIN L G. Introduction to "an arbitrary Lagrangian-Eulerian computing method for all flow speeds"[J]. Journal of Computational Physics, 1997, 135(2): 198-202.

MAIRE P H, BREIL J, GALERA S. A cell-centred arbitrary Lagrangian-Eulerian (ALE) method[J]. International Journal for Numerical Methods in Fluids, 2008, 56(8): 1161-1166.

LOUBERE R, MAIRE P H, SHASHKOV M, et al. ReALE: A reconnection-based arbitrary-Lagrangian-Eulerian method[J]. Journal of Computational Physics, 2010, 229(12): 4724-4761.

BARLOW A J, MAIRE P H, RIDER W J, et al. Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows[J]. Journal of Computational Physics, 2016, 322: 603-665.

PEERY J S, CARROLL D E. Multi-Material ALE methods in unstructured grids[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 187(3-4): 591-619.

WILKINS M L. Use of artificial viscosity in multidimensional shock wave problems[J]. J Comput Phys, 1980, 36(3): 281-303.

CARAMANA E J, BURTON D E, SHASHKOV M J, et al. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J]. Journal of Computational Physics, 1998, 146(1): 227-262.

MAIRE P H, LOUBÈRE R, VÁCHAL P. Staggered Lagrangian discretization based on cell-centered Riemann solver and associated hydrodynamics scheme[J]. Communications in Computational Physics, 2011, 10(4): 940-978.

MORGAN N R, LIPNIKOV K N, BURTON D E, et al. ALagrangian staggered grid Godunov-like approach for hydrodynamics[J]. Journal of Computational Physics, 2014, 259: 568-597.

GODUNOV S K. Reminiscences about difference schemes[J]. Journal of Computational Physics, 1999, 153(1): 6-25.

DESPRES B, MAZERAN C. Lagrangian gas dynamics in two dimensions and Lagrangian systems[J]. Archive for Rational Mechanics and Analysis, 2005, 178(3): 327-372.

CHENG J, SHU C W. A high order ENO conservative Lagrangian type scheme for the compressible Euler equations[J]. Journal of Computational Physics, 2007, 227(2): 1567-1596.

MAIRE P H, ABGRALL R, BREIL J, et al. A cell-centered Lagrangian scheme for two-dimensional compressible flow problems[J]. SIAM Journal on Scientific Computing, 2007, 29(4): 1781-1824.

MAIRE P H. A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes[J]. Journal of Computational Physics, 2009, 228(7): 2391-2425.

LOUBERE R, OVADIA J, ABGRALL R. A Lagrangian discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems[J]. International Journal for Numerical Methods in Fluids, 2004, 44(6): 645-663.

JIA Z, ZHANG S. A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions[J]. Journal of Computational Physics, 2011, 230(7): 2496-2522.

LI Z, YU X, JIA Z. The cell-centered discontinuousGalerkin method for Lagrangian compressible Euler equations in two-dimensions[J]. Computers Fluids, 2014, 96: 152-164.

KUCHARIK M, SHASHKOV M, WENDROFF B. An efficient linearity-and-bound-preserving remapping method[J]. Journal of Computational Physics, 2003, 188(2): 462-471.

GARIMELLA R, KUCHARIK M, SHASHKOV M. An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes[J]. Computers Fluids, 2007, 36(2): 224-237.

LOUBERE R, SHASHKOV M J. Asubcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods[J]. Journal of Computational Physics, 2005, 209(1): 105-138.

CHENG J, SHU C W. A high order accurate conservative remapping method on staggered meshes[J]. Applied Numerical Mathematics, 2008, 58(7): 1042-1060.

KUCHARIK M, SHASHKOV M. One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods[J]. Journal of Computational Physics, 2012, 231(7): 2851-2864.

DUKOWICZ J K, KODIS J W. Accurate conservative remapping (rezoning) for arbitrary Lagrangian-Eulerian computations[J]. SIAM Journal on Scientific and Statistical Computing, 1987, 8(3): 305-321.

GRANDY J. Conservative remapping and region overlays by intersecting arbitrarypolyhedra[J]. Journal of Computational Physics, 1999, 148(2): 433-466.

MENON S, SCHMIDT D P. Conservative interpolation on unstructured polyhedral meshes: An extension of thesupermesh approach to cell-centered finite-volume variables[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(41-44): 2797-2804.

JIA Z, LIU J, ZHANG S. An effective integration of methods for second-order three-dimensional multi-material ALE method on unstructured hexahedral meshes using MOF interface reconstruction[J]. Journal of Computational Physics, 2013, 236: 513-562.

KUCHARIK M, SHASHKOV M. Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods[J]. Journal of Computational Physics, 2014, 258: 268-304.

CHEN X, ZHANG X, JIA Z. A robust and efficient polyhedron subdivision and intersection algorithm for three-dimensional MMALE remapping[J]. Journal of Computational Physics, 2017, 338: 1-17.

BARLOW A J. A compatible finite element multi-material ALE hydrodynamics algorithm[J]. International Journal for Numerical Methods in Fluids, 2008, 56(8): 953-964.

GALERA S, MAIRE P H, BREIL J. A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction[J]. Journal of Computational Physics, 2010, 229(16): 5755-5787.

GALERA S, BREIL J, MAIRE P H. A 2D unstructured multi-material cell-centered arbitrary Lagrangian-Eulerian (CCALE) scheme using MOF interface reconstruction[J]. Computers Fluids, 2011, 46(1): 237-244.

BREIL J, GALERA S, MAIRE P H. Multi-material ALE computation in inertial confinement fusion code CHIC[J]. Computers Fluids, 2011, 46(1): 161-167.

JIA Z P, SUN Y T. A 2D cell-centered MMALE method based on MOF interface reconstruction[J]. Chinese Journal of Computational Physics, 2016, 33(5): 523-538. (in Chinese)

RIDER W J, MARGOLIN L G. Simple modifications of monotonicity-preserving limiter[J]. Journal of Computational Physics, 2001, 174(1): 473-488.

BLANCHARD G, LOUBERE R. High order accurate conservative remapping scheme on polygonal meshes using a posteriori MOOD limiting[J]. Computers Fluids, 2016, 136: 83-103.

CLAIN S, DIOT S, LOUBERE R. A high-order finite volume method for systems of conservation laws-Multi-dimensional Optimal Order Detection (MOOD)[J]. Journal of computational Physics, 2011, 230(10): 4028-4050.

DIOT S, CLAIN S, LOUBERE R. Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials[J]. Computers Fluids, 2012, 64: 43-63.

AULISA E, MANSERVISI S, SCARDOVELLI R, et al. Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry[J]. Journal of Computational Physics, 2007, 225(2): 2301-2319.

TIPTON R E. CALE mixed zone pressure relaxation model[R]. Tech rep, Private communication, Lawrence Livermore National Laboratory, 1989: 82.

SHASHKOV M. Closure models formultimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes[J]. International Journal for Numerical Methods in Fluids, 2008, 56(8): 1497-1504.

KUCHARIK M, GARIMELLA R V, SCHOFIELD S P, et al. A comparative study of interface reconstruction methods for multi-material ALE simulations[J]. Journal of Computational Physics, 2010, 229(7): 2432-2452.

QING F, YU X, JIA Z. A robust MoF method applicable to severely deformed polygonal mesh[J]. Journal of Computational Physics, 2019, 377: 162-182.

KNUPP P M. Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I-A framework for surface mesh optimization[J]. International Journal for Numerical Methods in Engineering, 2000, 48(3): 401-420.

STROUBOULIS T, DEVLOO P, ODEN J T. A moving-grid finite element algorithm for supersonic flow interaction between moving bodies[J]. Computer Methods in Applied Mechanics and Engineering, 1986, 59(2): 235-255.

COCKBURN B, SHU C W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems[J]. Journal of Computational Physics, 1998, 141(2): 199-224.

BARTH T J. Numerical methods for gasdynamic systems on unstructured meshes[M]//An introduction to recent developments in theory and numerics for conservation laws. Springer, Berlin, Heidelberg, 1999: 195-285.

DYADECHKO V, SHASHKOV M. Moment-of-fluid interface reconstruction[J]. Los Alamos Report LA-UR-05-7571, 2005.

CHEN X, ZHANG X. An improved 2D MoF method by using high order derivatives[J]. Journal of Computational Physics, 2017, 349: 176-190.

MAVRIPLIS D. Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes[C]//16th AIAA Computational Fluid Dynamics Conference. 2003: 3986.

YOUNGS D L. Multi-mode implosion in cylindrical 3d geometry[C]//11th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM11), Santa Fe. 2008.

SEDOV L I. Similarity and dimensional methods in mechanics[M]. New York: Academic Press, 1959.

QUIRK JJ, KARNI S. On the dynamics of a shock-bubble interaction[J]. Journal of Fluid Mechanics, 1996, 318: 129-163.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Dynamic ablation morphology measurement of thermal protection materials using structured light vision

Impact of inter-wing spacing on aerodynamic noise in multi-flapping wing configurations

Analysis of damping and cross dynamic derivative characteristics for a quasi-HyTRV lifting body

Noise prediction and reduction methods for LAGOON landing gear based on Lattice Boltzmann method

Multi-factor analysis and simulation of particle erosion characteristics of fan blades

Related Author

No data

Related Institution

No data

AI问答

⁰