A Novel Full-Euler Low Mach Number IMEX Splitting

K. Kaiser has been partially supported by the German Research Foundation (DFG) through project NO 361/6-1; his study was supported by the Special Research Fund (BOF) of Hasselt University. M. Lukacova has been partially supported by the TRR 165 "Waves to weather". J. Zeifang has been supported by the German Research Foundation (DFG) through the International Research Training Group GRK 2160/1: Droplet Interaction Technologies. We acknowledge the support and the computing time provided by the High Performance Computing Center Stuttgart (HLRS) through the hpcdg project.

[1]  Shi Jin.  ASYMPTOTIC PRESERVING (AP) SCHEMES FOR MULTISCALE KINETIC AND HYPERBOLIC EQUATIONS: A REVIEW , 2010 .

[2]  E Weinan,et al.  A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow , 1992 .

[3]  Lorenzo Pareschi,et al.  Implicit-Explicit Runge-Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit , 2013, SIAM J. Sci. Comput..

[4]  Claus-Dieter Munz,et al.  Explicit Discontinuous Galerkin methods for unsteady problems , 2012 .

[5]  Mária Lukácová-Medvid'ová,et al.  Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation , 2017, J. Comput. Phys..

[6]  David A. Kopriva,et al.  Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers , 2009 .

[7]  Philip M. Gresho,et al.  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. Part 1: Theory , 1990 .

[8]  Claus-Dieter Munz,et al.  Efficient high-order discontinuous Galerkin computations of low Mach number flows , 2018, Communications in Applied Mathematics and Computational Science.

[9]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[10]  P. Roe.  CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[11]  Claus-Dieter Munz,et al.  A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics , 2014, SIAM J. Sci. Comput..

[12]  Wasilij Barsukow,et al.  A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics , 2016, Journal of Scientific Computing.

[13]  Emil M. Constantinescu,et al.  Semi-Implicit Time Integration of Atmospheric Flows with Characteristic-Based Flux Partitioning , 2015, SIAM J. Sci. Comput..

[14]  Michael Dumbser,et al.  A conservative, weakly nonlinear semi-implicit finite volume scheme for the compressible Navier-Stokes equations with general equation of state , 2016, Appl. Math. Comput..

[15]  R. Hartmann,et al.  Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations , 2002 .

[16]  Klaus Kaiser,et al.  A New Stable Splitting for the Isentropic Euler Equations , 2016, Journal of Scientific Computing.

[17]  Willem Hundsdorfer,et al.  IMEX extensions of linear multistep methods with general monotonicity and boundedness properties , 2007, J. Comput. Phys..

[18]  Jian‐Guo Liu,et al.  An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations , 2012 .

[19]  J. Anderson,et al.  Fundamentals of Aerodynamics , 1984 .

[20]  S. Schochet.  The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit , 1986 .

[21]  Baolin Tian,et al.  A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations , 2018 .

[22]  Steven J. Ruuth,et al.  Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations , 1997 .

[23]  Feng Xiao,et al.  A Direct ALE Multi-Moment Finite Volume Scheme for the Compressible Euler Equations , 2018 .

[24]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[25]  Klaus Kaiser,et al.  A High-Order Method for Weakly Compressible Flows , 2017 .

[26]  Pierre Degond,et al.  An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations , 2011, J. Comput. Phys..

[27]  Claus-Dieter Munz,et al.  Comparison of Different Splitting Techniques for the Isentropic Euler Equations , 2018 .

[28]  Sebastian Noelle,et al.  IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows , 2014 .

[29]  R. Klein.  Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics , 1995 .

[30]  SEBASTIANO BOSCARINO.  Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems , 2007, SIAM J. Numer. Anal..

[31]  Michael Dumbser,et al.  A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers , 2016, J. Comput. Phys..

[32]  A. Majda,et al.  Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit , 1981 .

[33]  Giovanni Russo,et al.  All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics , 2017, Journal of Scientific Computing.

[34]  S. Jin,et al.  MACH-NUMBER UNIFORM ASYMPTOTIC-PRESERVING GAUGE SCHEMES FOR COMPRESSIBLE FLOWS , 2007 .

[35]  Jun Zou,et al.  Some new additive Runge-Kutta methods and their applications , 2006 .

[36]  Hamed Zakerzadeh.  Asymptotic analysis of the RS-IMEX scheme for the shallow water equations in one space dimension , 2019, ESAIM: Mathematical Modelling and Numerical Analysis.

[37]  Claus-Dieter Munz,et al.  Efficient Parallelization of a Shock Capturing for Discontinuous Galerkin Methods using Finite Volume Sub-cells , 2017, J. Sci. Comput..