| [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]. SIAM Journal on Numerical Analysis, 1994, 31:17-42.[57] von Neumann J, Richtmyer R. A method for the calculation of hydrodynamics shocks[J]. Journal of Applied Physics, 1950, 21:232-237.[58] Ortega A, Scovazzi G. A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian-Eulerian computations with nodal finite elements[J]. Journal of Computational Physics, 2011, 230:6709-6741.[59] Perthame B, Shu C W. On positivity preserving finite volume schemes for Euler equations[J]. Numerische Mathematik, 1996, 73:119-130.[60] Scovazzi G, Christon M, Hughes T, Shadid J. Stabilized shock hydrodynamics:I. A Lagrangian method[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196:923-966.[61] Scovazzi G. Stabilized shock hydrodynamics:II. Design and physical interpretation of the SUPG operator for Lagrangian computations[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196:966-978.[62] Scovazzi G. Lagrangian shock hydrodynamics on tetrahedral meshes:A stable and accurate variational multiscale approach[J]. Journal of Computational Physics, 2012, 231:8029-8069.[63] Shu C W, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J]. Journal of Computational Physics, 1988, 77:439-471.[64] Toro E. Riemann solvers and numerical methods for fluid dynamics[M]. Springer-Verlag, Berlin, 1999.[65] Wilkins M. Calculation of elastic plastic flow[J]. Methods of Computational Physics, 1964, 3:211-263.[66] Vilar F, Maire P H, Abgrall R. Cell-centered discontinuous Galerkin discretizations for twodimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics[J]. Computers & Fluids, 2011, 46:498-504.[67] Vilar F. Cell-centered discontinuous Galerkin discretization for two dimensional Lagrangian hydrodynamics[J]. Computers & Fluids, 2012, 64:64-73.[68] Vilar F, Maire P H, Abgrall R. A discontinuous Galerkin discretization for solving the twodimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids[J]. Journal of Computational Physics, 2014, 276:188-234.[69] Vilar F, Shu C W, Maire P H. Positivity-preserving cell-centered Lagrangian schemes for multimaterial compressible flows:From first-order to high-orders. Part I:The one-dimensional case[J]. Journal of Computational Physics, 2016, 312:385-415.[70] Vilar F, Shu C W, Maire P H. Positivity-preserving cell-centered Lagrangian schemes for multimaterial compressible flows:From first-order to high-orders. Part II:The two-dimensional case[J]. Journal of Computational Physics, 2016, 312:416-442.[71] Wang C W, Liu T G, and B C. KhooA Real Ghost Fluid Method for the Simulation of Multimedium Compressible Flow[J]. SIAM Journal on Scientific Computing, 2006, 28:278-302.[72] Zhu J, Shu C W. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy[J]. Journal of Computational Physics, 2018, 375:659-683.[73] Zhu J, Shu C W. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes[J]. Journal of Computational Physics, 2019, 392:19-33.[74] Zhang R, Zhang M, Shu C W. On the order of accuracy and numerical performance of two classes of finite volume WENO schemes[J]. Communications in Computational Physics, 2011, 9:807-827.[75] Zhang X, Shu C W. On positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes[J]. Journal of Computational Physics, 2010, 229:8918-8934.[76] Zhang X, Shu C W. Positivity preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms[J]. Journal of Computational Physics, 2011, 230:1238-1248.[77] Zhang X, Shu C W. Maximum-principle-satisfying and positivity preserving high order schemes for conservation laws:Survey and new developments[J]. Proceedings of the Royal Society A, 2011, 467:2752-2776.[78] Zhang X, Shu C W. Positivity preserving high order finite difference WENO schemes for compressible Euler equations[J]. Journal of Computational Physics, 2012, 231:2245-2258. |
