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

by   Liang Yin, et al.

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.


page 26

page 27


A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions

The present work proposes a second-order time splitting scheme for a lin...

Parallel energy-stable phase field crystal simulations based on domain decomposition methods

In this paper, we present a parallel numerical algorithm for solving the...

Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations

We focus here on a class of fourth-order parabolic equations that can be...

A Kernel-free Boundary Integral Method for the Bidomain Equations

The bidomain equations have been widely used to mathematically model the...

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in heterogeneous tissue models

We report the first implementation of the Lattice Boltzmann method (LBM)...

Real-World Oceanographic Simulations on the GPU using a Two-Dimensional Finite-Volume Scheme

In this work, we take a modern high-resolution finite-volume scheme for ...

Please sign up or login with your details

Forgot password? Click here to reset