Efficient Random Walk Algorithm for Simulating Thermal Transport in Composites With High Conductivity Contrast

TL;DR

This paper presents an improved random walk algorithm for simulating thermal transport in composites with high conductivity contrast, enabling faster computations while maintaining physical laws.

Contribution

It introduces a modified random walk method that efficiently handles high conductivity contrasts, including the infinite conductivity limit, in thermal transport simulations.

Findings

Algorithm accelerates simulations in high contrast composites.

Preserves second law of thermodynamics in the modified approach.

Validated in 1D and 3D composite systems.

Abstract

In dealing with thermal transport in composite systems, high contrast materials pose a special problem for numerical simulation: the time scale or step size in the high conductivity material must be much smaller than in the low conductivity material. In the limit that the higher conductivity inclusion can be treated as having an infinite conductivity, we show how a standard random walk algorithm can be alterred to improve speed while still preserving the second law of thermodynamics. We demonstrate the principle in a 1D system, and then apply it to 3D composites with spherical inclusions.