A stochastic approach to the solution of magnetohydrodynamic equations

TL;DR

This paper introduces a stochastic method for solving magnetohydrodynamic equations, enabling localized solutions and efficient parallel computation, demonstrated through generating long-range magnetic fields.

Contribution

It presents a novel stochastic solution approach for magnetohydrodynamics equations, with details on numerical implementation and an illustrative example.

Findings

Successful generation of long-range magnetic fields

Efficient localized solutions in configuration space

Potential for parallel computation in MHD simulations

Abstract

The construction of stochastic solutions is a powerful method to obtain localized solutions in configuration or Fourier space and for parallel computation with domain decomposition. Here a stochastic solution is obtained for the magnetohydrodynamics equations. Some details are given concerning the numerical implementation of the solution which is illustrated by an example of generation of long-range magnetic fields by a velocity source.