An efficient particle locating method on unstructured meshes in two and three dimensions based on patch searching

TL;DR

This paper introduces a fast and robust particle locating method on unstructured meshes in 2D and 3D, utilizing patch searching and auxiliary grids to improve efficiency and simplicity.

Contribution

The proposed method efficiently locates particles on unstructured meshes using patch searching and auxiliary grids, requiring only particle coordinates, which enhances robustness and speed.

Findings

Method is robust in 2D and 3D scenarios.

Significant reduction in search time demonstrated.

Applicable to complex unstructured meshes.

Abstract

We present a particle locating method for unstructured meshes in two and three dimensions. Our algorithm is based on a patch searching process, and includes two steps. We first locate the given point to a patch near a vertex, and then the host element is determined within the patch domain. Here, the patch near a vertex is the domain of elements around this vertex. We prove that in the first step the patch can be rapidly identified by constructing an auxiliary Cartesian grid with a prescribed resolution. Then, the second step can be converted into a searching problem, which can be easily solved by searching algorithms. Only coordinates to particles are required in our method. We conduct a series of numerical tests in two and three dimensions to illustrate the robustness and efficiency of our method.