A low-Mach number fix for Roe’s approximate Riemann solver

Journal of Computational Physics - Tập 230 - Trang 5263-5287 - 2011
Felix Rieper1
1Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany

Tài liệu tham khảo

Sesterhenn, 1999, On the cancellation problem in calculating compressible low Mach number flows, J. Comput. Phys., 151, 597, 10.1006/jcph.1999.6211 LeVeque, 2002 Turkel, 1987, Preconditioned methods for solving the incompressible and low speed compressible equations, J. Comput. Phys., 72, 277, 10.1016/0021-9991(87)90084-2 Turkel, 1995, Preconditioning and the limit of the compressible to the incompressible flow equations for finite difference schemes, 215 van Leer, 1991, Characteristic time-stepping or local preconditioning of the euler equations, AIAA paper, 91 Choi, 1993, The application of preconditioning in viscous flows, J. Comput. Phys., 105, 207, 10.1006/jcph.1993.1069 Guillard, 1999, On the behaviour of upwind schemes in the low Mach number limit, Comput. Fluids, 28, 63, 10.1016/S0045-7930(98)00017-6 Li, 2008, An all-speed Roe-type scheme its asymptotic analysis of low Mach number behaviour., J. Comput. Phys., 227, 5144, 10.1016/j.jcp.2008.01.037 Birken, 2005, Stability of preconditioned finite volume schemes at low Mach numbers, BIT, 45, 463, 10.1007/s10543-005-0009-0 Dellacherie, 2010, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, J. Comput. Phys., 229, 978, 10.1016/j.jcp.2009.09.044 Feistauer, 2007, On a robust discontinuous Galerkin technique for the solution of compressible flow, J. Comput. Phys., 224, 208, 10.1016/j.jcp.2007.01.035 Bassi, 2009, A discontinuous Galerkin method for inviscid low Mach number flows, J. Comput. Phys., 228, 3996, 10.1016/j.jcp.2009.02.021 Thornber, 2008, On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes, J. Comput. Phys., 227, 4853, 10.1016/j.jcp.2008.01.035 Thornber, 2008, An improved reconstruction method for compressible flows with low Mach number features, J. Comput. Phys., 227, 4873, 10.1016/j.jcp.2008.01.036 C. Viozat, Implicit Upwind Schemes for Low Mach Number Compressible Flows, Technical report, Institut National de Recherche en Informatique et en Automatique (INRIA), 1997. Rhie, 1983, Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J., 21, 1525, 10.2514/3.8284 Rieper, 2009, The influence of cell geometry on the accuracy of upwind schemes in the low Mach number regime, J. Comput. Phys., 228, 2918, 10.1016/j.jcp.2009.01.002 Guillard, 2009, On the behavior of upwind schemes in the low Mach number limit. IV: P0 Approximation on triangular and tetrahedral cells, Comput. Fluids, 38, 1969, 10.1016/j.compfluid.2009.06.003 Guillard, 2004, On the behavior of upwind schemes in the low Mach number limit. II: Godunov type schemes, Comput. Fluids, 33, 655, 10.1016/j.compfluid.2003.07.001 Dellacherie, 2010, The influence of cell geometry on the Godunov scheme applied to the linear wave equation, J. Comput. Phys., 229, 5315, 10.1016/j.jcp.2010.03.012 Tapp, 1976, A non-hydrostatic mesoscale model, Quart. J. Roy. Meteor. Soc., 102, 277, 10.1002/qj.49710243202 Durran, 1998, 32 F. Fillion, A. Chanoine, S. Dellacherie, A. Kumbaro, FLICA-OVAP: a new platform for core thermal-hydraulic studies, in: 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-13), 2009. A. Meister, Analyse und Anwendung Asymptotik-basierter numerischer Verfahren zur Simulation reibungsbehafteter Strömungen in allen Mach-Zahlbereichen, Habilitationsschrift, Universität Hamburg, 2001. Klein, 1995, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I: one-dimensional flow, J. Comput. Phys., 121, 213, 10.1016/S0021-9991(95)90034-9 Klainerman, 1982, Compressible and incompressible fluids, Commun. Pure Appl. Math., 35, 629, 10.1002/cpa.3160350503 S. Dellacherie, Checkerboard modes and wave equation, in: Proceedings of ALGORITMY 2009, 2009, pp. 71–80. Gresho, 1990, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. II: Implementation, Int. J. Numer. Methods Fluids, 11, 621, 10.1002/fld.1650110510 Gresho, 1990, On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. I: Theory, Int. J. Numer. Methods Fluids, 11, 587, 10.1002/fld.1650110509 Rieper, 2010, On the dissipation mechanism of upwind-schemes in the low Mach number regime: a comparison between Roe and HLL, J. Comput. Phys., 229, 221, 10.1016/j.jcp.2009.09.043 Laney, 1998 Sod, 1978, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys., 27, 1, 10.1016/0021-9991(78)90023-2 Lax, 1954, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Commun. Pure Appl. Math., 7, 159, 10.1002/cpa.3160070112 Toro, 1999 Einfeldt, 1987, Ein schneller Algorithmus zur Lösung des Riemann-problems. (An efficient algorithm for the solution to the Riemann problem), Computing, 39, 77, 10.1007/BF02307715 Shu, 1998, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, vol. 1697, 325 S. Vater, Private communication, FU Berlin, 2010.