Parallel finite volume simulation of the spherical shell dynamo with pseudo-vacuum magnetic boundary conditions

TL;DR

This paper presents a scalable parallel finite volume method for simulating the spherical shell dynamo with pseudo-vacuum magnetic boundary conditions, demonstrating high efficiency and scalability on supercomputers.

Contribution

It introduces a novel parallel finite volume scheme with a multi-level preconditioner for efficient large-scale MHD dynamo simulations in spherical shells.

Findings

Achieved accurate solutions comparable to existing methods.

Demonstrated good scalability on supercomputers with up to 10368 cores.

Improved computational efficiency with a multi-level preconditioner.

Abstract

In this paper, we study the parallel simulation of the magnetohydrodynamic (MHD) dynamo in a rapidly rotating spherical shell with pseudo-vacuum magnetic boundary conditions. A second-order finite volume scheme based on a collocated quasi-uniform cubed-sphere grid is applied to the spatial discretization of the MHD dynamo equations. To ensure the solenoidal condition of the magnetic field, we adopt a widely-used approach whereby a pseudo-pressure is introduced into the induction equation. The temporal integration is split by a second-order approximate factorization approach, resulting in two linear algebraic systems both solved by a preconditioned Krylov subspace iterative method. A multi-level restricted additive Schwarz preconditioner based on domain decomposition and multigrid method is then designed to improve the efficiency and scalability. Accurate numerical solutions of two benchmark cases are obtained with our code, comparable to the existing local method results. Several large-scale tests performed on the Sunway TaihuLight supercomputer show good strong and weak scalabilities and a noticeable improvement from the multi-level preconditioner with up to 10368 processor cores.