Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics

Authors:
Friedrich Kupka;Natalie Happenhofer;Inmaculada Higueras;Othmar Koch
Affiliations:
University of Vienna, Faculty of Mathematics, Nordbergstraíe 15, A-1090 Wien, Austria;University of Vienna, Faculty of Mathematics, Nordbergstraíe 15, A-1090 Wien, Austria;Universidad Pública de Navarra, Departamento de Ingeniería Matemática e Informática, Campus de Arrosadia, 31006 Pamplona, Spain;Vienna University of Technology, Institute for Analysis and Scientific Computing, A-1040 Wien, Austria
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit-explicit Runge-Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in the simulation of stellar convection. The fully compressible Navier-Stokes equation, augmented by continuity and total energy equations, and an equation of state describing the relation between the thermodynamic quantities, is semi-discretized in space by essentially non-oscillatory schemes and dissipative finite difference methods. It is subsequently integrated in time by Runge-Kutta methods which are constructed such as to preserve the total variation diminishing (or strong stability) property satisfied by the spatial discretization coupled with the forward Euler method. We analyse the stability, accuracy and dissipativity of the time integrators and demonstrate that the most successful methods yield a substantial gain in computational efficiency as compared to classical explicit Runge-Kutta methods.