Multiscale Random-Walk Algorithm for Simulating Interfacial Pattern Formation

TL;DR

This paper introduces a new multiscale random-walk algorithm that accurately simulates complex interfacial pattern formation, including 3D dendritic growth at low undercoolings, which was previously computationally challenging.

Contribution

The paper presents a novel multiscale random-walk computational method capable of simulating complex interfacial patterns across a wide range of scales.

Findings

Successfully simulated 3D dendritic growth at low undercoolings.

Demonstrated the method's ability to handle large-scale diffusion-limited growth.

Validated the simulation results against experimental conditions.

Abstract

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.