A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics

Physics-based preconditioning for sound waves and thermal diffusion

¹ Max-Planck Institut für Astrophysik, Karl Schwarzschild Strasse 1, 85741 Garching, Germany
e-mail: mviallet@mpa-garching.mpg.de
² College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
³ École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, Lyon France

Received: 10 September 2015
Accepted: 7 December 2015

Abstract

This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10^-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.