Error analysis of the Monte Carlo method for compressible magnetohydrodynamics

TL;DR

This paper analyzes the accuracy of a combined Monte Carlo and finite volume approach for simulating random compressible viscous magnetohydrodynamic flows, providing error estimates and convergence results.

Contribution

It introduces a novel numerical framework with error analysis for stochastic magnetohydrodynamics, demonstrating convergence and illustrating complex dynamics.

Findings

Error estimates for statistical and deterministic errors

Convergence of numerical solutions up to the solution's lifespan

Numerical experiments reveal rich dynamics of the flows

Abstract

We study random compressible viscous magnetohydrodynamic flows. Combining the Monte Carlo method with a deterministic finite volume method we solve the random system numerically. Quantitative error estimates including statistical and deterministic errors are analyzed up to a stopping time of the exact solution. On the life-span of an exact strong solution we prove the convergence of the numerical solutions. Numerical experiments illustrate rich dynamics of random viscous compressible magnetohydrodynamics.