计算数学
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计算数学  2020, Vol. 42 Issue (3): 261-278    DOI:
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可压缩流体力学高精度拉格朗日格式及其保正性质
成娟1,2, 舒其望3
1 国防计算物理实验室, 北京应用物理与计算数学研究所, 北京 100088;
2 京大学应用物理与技术中心, 北京 100871;
3 美国布朗大学应用数学系, 罗德岛州 RI 02912, 美国
HIGH ORDER LAGRANGIAN SCHEMES AND THEIR POSITIVITY-PRESERVING PROPERTY FOR COMPRESSIBLE FLUID FLOW
Cheng Juan1,2, Shu Chi-Wang3
1 Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2 Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
3 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
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摘要 本文对可压缩流体力学高精度拉格朗日格式及其保正性质近年来的发展给出回顾与综述.文中分别介绍了一维、二维可压缩流体力学方程中心型拉格朗日格式的设计步骤,回顾了高精度拉格朗日格式以及高精度保正拉格朗日格式的研究进展.
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关键词拉格朗日格式   高精度   保正   可压缩   流体力学     
Abstract: This paper gives a survey on the recent development of high order Lagrangian schemes for solving compressible Euler equations and their positivity-preserving property. We introduce the major steps in the design of one and two-dimensional cell-centered Lagrangian schemes and review the research developments of high order Lagrangian schemes and the methodology to achieve the positivity-preserving performance.
Key wordsLagrangian schemes   high order   positivity-preserving   compressible   fluid flow   
收稿日期: 2020-03-17;
基金资助:

国家自然科学基金(11871111,U1630247)、国防基础科研核基础科学挑战计划(TZ2016002)和中国工程物理研究院创新发展基金资助项目(CX20200026)资助.

引用本文:   
. 可压缩流体力学高精度拉格朗日格式及其保正性质[J]. 计算数学, 2020, 42(3): 261-278.
. HIGH ORDER LAGRANGIAN SCHEMES AND THEIR POSITIVITY-PRESERVING PROPERTY FOR COMPRESSIBLE FLUID FLOW[J]. Mathematica Numerica Sinica, 2020, 42(3): 261-278.
 
[1] Abgrall R, Loubere R, Ovadia J. A Lagrangian discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems[J]. International Journal for Numerical Methods in Fluids, 2004, 44:645-663.
[2] Balsara D. Multidimensional HLLE Riemann solver:application to Euler and magnetohydrodynamic flows[J]. Journal of Computational Physics, 2010, 229:1970-1993.
[3] Barlow A, Maire P H, Rider W, Rieben R, Shashkov M. Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multi-material flows[J]. Journal of Computational Physics, 2016, 322:603-665.
[4] Batten P, Clarke N, Lambert C, Causon D. On the choice of wavespeeds for the HLLC Riemann solver[J]. SIAM Journal on Scientific Computing, 1997, 18:1553-1570.
[5] Benson D. Computational methods in Lagrangian and Eulerian hydrocodes[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 99:235-394.
[6] Bezard F, Despres B. An entropic solver for ideal Lagrangian magnetohydrodynamics[J]. Journal of Computational Physics, 1999, 154:65-89.
[7] Boscheri W, Dumbser M. Arbitrary-Lagrangian-Eulerian one-step WENO finite volume schemes on unstructured triangular meshes[J]. Communications in Computational Physics, 2013, 14:1174-1206.
[8] Boscheri W, Balsara D, Dumbser M. Lagrangian ADER-WENO finite volume schemes on unstructured triangular meshes based on genuinely multidimensional HLL Riemann solvers[J]. Journal of Computational Physics, 2014, 267:112-138.
[9] Boscheri W, Dumbser M, Balsara D. High order Lagrangian ADER-WENO schemes on unstructured meshes-Application of several node solvers to hydrodynamics and magnetohydrodynamics[J]. International Journal for Numerical Methods in Fluids, 2014, 76:737-778.
[10] Boscheri W, Dumbser M. A direct arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and nonconservative hyperbolic systems in 3D[J]. Journal of Computational Physics, 2014, 275:484-523.
[11] Boscheri W, Dumbser M, Zanotti O. High order cell-centered Lagrangian-type finite volume schemes with time-accurate local time stepping on unstructured triangular meshes[J]. Journal of Computational Physics, 2015, 291:120-150.
[12] Burton D. Multidimensional discretization of conservation laws for unstructured polyhedral grids, Technical Report UCRL-JC-118306, Lawrence Liver-more National Laboratory, 1994.
[13] Caramana E, Burton D, Shashkov M, Whalen P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, Journal of Computational Physics[J]. 1998, 146:227-262.
[14] Caramana E, Shashkov M, Whalen P. Formulations of artificial viscosity for multidimensional shock wave computations[J]. Journal of Computational Physics, 1998, 144:70-97.
[15] Carre G, Del Pino S, Despres B, Labourasse E. A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension[J]. Journal of Computational Physics, 2009, 228:5160-5183.
[16] Cheng J, Shu C W. A high order ENO conservative Lagrangian type scheme for the compressible Euler equations[J]. Journal of Computational Physics, 2007, 227:1567-1596.
[17] Cheng J, Shu C W. A third order conservative Lagrangian type scheme on curvilinear meshes for the compressible Euler equation[J]. Communications in Computational Physics, 2008, 4:1008-1024.
[18] Cheng J, Shu C W. A high order accurate conservative remapping method on staggered meshes[J]. Applied Numerical Mathematics, 2008, 58:1042-1060.
[19] Cheng J, Shu C W. A cell-centered Lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two-dimensional cylindrical geometry[J]. Journal of Computational Physics, 2010, 229:7191-7206.
[20] Cheng J, Shu C W. Improvement on spherical symmetry in two-dimensional cylindrical coordinates for a class of control volume Lagrangian schemes[J]. Communications in Computational Physics, 2012, 11:1144-1168.
[21] Cheng J, Shu C W, Zeng Q. A conservative Lagrangian scheme for solving compressible fluid flows with multiple internal energy equations[J]. Communications in Computational Physics, 2012, 12:1307-1328.
[22] Cheng J, Shu C W. Positivity-preserving Lagrangian scheme for multi-material compressible flow[J]. Journal of Computational Physics, 2014, 257:143-168.
[23] Cheng J, Shu C W. Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates[J]. Journal of Computational Physics, 2014, 272:245-265.
[24] Cockburn B, Karniadakis G, Shu C W. The development of discontinuous Galerkin methods, Part I:Overview, in:B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods:Theory, Computation and Applications, in:Lecture Notes in Computational Science and Engineering, 2000, 11:Springer, 3-50.
[25] Despres B, Mazeran C. Symmetrization of lagrangian gas dynamic in dimension two and multimdimensional solvers[J]. C. R. Mecanique, 2003, 331:475-480.
[26] Despres B, Mazeran C. Lagrangian gas dynamics in two dimensions and Lagrangian systems[J]. Archive for Rational Mechanics and Analysis, 2005, 178:327-372.
[27] Dobrev V, Ellis T, Kolev T, Rieben R. Curvilinear finite elements for Lagrangian hydrodynamics[J]. International Journal for Numerical Methods in Fluids, 2011, 65:1295-1310.
[28] Dobrev V, Ellis T, Kolev T, Rieben R. High order curvilinear finite elements for Lagrangian hydrodynamics[J]. SIAM Journal on Scientific Computing, 2012, 34:606-641.
[29] Dobrev V, Ellis T, Kolev T, Rieben R. High order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics[J]. Computers & Fluids, 2013, 83:58-69.
[30] Dukowicz J. A general, non-iterative Riemann solver for Godunov method[J]. Journal of Computational Physics, 1985, 61:119-137.
[31] Dukowicz J, Baumgardener J. Incremental remapping as a transport/advection algorithm[J]. Journal of Computational Physics, 2000, 160:318-335.
[32] Dumbser M, Uuriintsetseg A, Zanotti O. On arbitrary-Lagrangian-Eulerian one-step WENO schemes for stiff hyperbolic balance laws[J]. Communications in Computational Physics, 2013, 14:301-327.
[33] Dumbser M, Boscheri W. High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems:Applications to compressible multi-phase flows[J]. Computers & Fluids, 2013, 86:405-432.
[34] Gaburro E, Boscheri W, Chiocchetti S, Klingenberg C, Springel V, Dumbser M. High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes[J]. Journal of Computational Physics, 2020, 407:109-167,
[35] Einfeldt B, Munz C, Roe P, Sjogreen B. On Godunov-type methods near low densities[J]. Journal of Computational Physics, 1991, 92:273-295.
[36] Gallice G. Positive and entropy stable Godunov-type schemes for gas dynamics and MHD equations in Lagrangian or Eulerian coordinates[J]. Numerische Mathematik, 2003, 94:673-713.
[37] Harten A, Engquist B, Osher S, Chakravarthy S. Uniformly high order accurate essentially nonoscillatory schemes, III[J]. Journal of Computational Physics, 1987, 71:231-303.
[38] Hirt C, Amsden A, Cook J. An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics, 1974, 14:227-253.
[39] 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, 230:2496-2522.
[40] Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes[J]. Journal of Computational Physics, 1996, 126:202-228.
[41] Ling D, Cheng J, Shu C W. Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates[J]. Computers & Fluids, 2017, 157:112-130.
[42] Liou M. A sequel to AUSM:AUSM+[J]. Journal of Computational Physics, 1996, 129:364-382.
[43] Liu W, Cheng J, Shu C W. High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations[J]. Journal of Computational Physics, 2009, 228:8872-8891.
[44] Liu X, Osher S, Chan T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115:200-212.
[45] Liu X, Morgan N, Burton D. A Lagrangian discontinuous Galerkin hydrodynamic method[J]. Computers & Fluids, 2018, 163:68-85.
[46] Liu X, Morgan N, Burton D. A high-order Lagrangian discontinuous Galerkin hydrodynamic method for quadratic cells using a subcell mesh stabilization scheme[J]. Journal of Computational Physics, 2019, 386:110-157.
[47] Loubere R, Shashkov M. A subcell remapping method on staggered polygonal grids for arbitraryLagrangian-Eulerian methods[J]. Journal of Computational Physics, 2005, 209:105-138.
[48] Maire P H, Abgrall R, Breil J, Ovadia J. A cell-centered Lagrangian scheme for compressible flow problems[J]. SIAM Journal of Scientific Computing, 2007, 29:1781-1824.
[49] Maire P H, Nkonga B. Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics[J]. Journal of Computational Physics, 2009, 228:799-821.
[50] 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, 228:2391-2425.
[51] Maire P H. A high-order cell-centered Lagrangian scheme for compressible fluid flows in twodimensional cylindrical geometry[J]. Journal of Computational Physics, 2009, 228:6882-6915.
[52] Maire P H, Loubere R, Vachal P. Staggered Lagrangian discretization based on cell-centered Riemann solver and associated hydrodynamics scheme[J]. Communications in Computational Physics, 2011, 10:940-978.
[53] Margolin L and Shashkov M. Second-order sign-preserving conservative interpolation (remapping) on general grids[J]. Journal of Computational Physics, 2003, 184:266-298.
[54] Morgan N, Lipnikov K, Burton D, Kenamond M. A Lagrangian staggered grid Godunov-like approach for hydrodynamics[J]. Journal of Computational Physics, 2014, 259:568-597.
[55] Morgan N, Liu X, Burton D. Reducing spurious mesh motion in Lagrangian finite volume and discontinuous Galerkin hydrodynamic methods[J]. Journal of Computational Physics, 2018, 372:35-61.
[56] Munz C. On Godunov-type schemes for Lagrangian gas dynamics[J]. SI