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

TL;DR

This paper introduces a Jacobian-free Newton-Krylov implicit solver tailored for multidimensional stellar hydrodynamics, enabling efficient simulation of turbulent processes in stellar interiors with high Mach numbers.

Contribution

It presents a novel combination of Jacobian-free Newton-Krylov methods with specialized preconditioning for stellar hydrodynamics, applicable to 2D and 3D flows.

Findings

Accurately models flows with Mach numbers as low as 10^{-6}

Demonstrates efficiency in multidimensional stellar interior simulations

Enables new 3D studies of stellar structure and evolution

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.