A mesh-constrained discrete point method for incompressible flows with moving boundaries

TL;DR

This paper introduces a novel meshless method for simulating incompressible flows with moving boundaries, improving particle distribution and computational efficiency by extending the mesh-constrained discrete point approach.

Contribution

It develops a new updating algorithm for particle arrangement in moving boundary problems, enhancing the original MCD method for better accuracy and efficiency.

Findings

Achieved good performance in moving boundary flow simulations.

Maintained uniform particle distribution during boundary movements.

Enhanced computational efficiency over traditional particle methods.

Abstract

Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which is enhanced over time and result in problems in computational efficiency and parallel computations. To mitigate these problems, a mesh-constrained discrete point (MCD) method was developed for stationary boundary problems (Matsuda et al., 2022). Although the MCD method is a meshless method that uses moving least-squares approximation, the arrangement of particles (or discrete points (DPs)) is specialized so that their positions are constrained in background meshes to obtain a closely uniform distribution. This achieves a reasonable approximation for spatial derivatives with compact stencils without encountering any ill-posed condition and leads to good performance in terms of computational efficiency. In this study, a novel meshless method based on the MCD method for incompressible flows with moving boundaries is proposed. To ensure the mesh constraint of each DP in moving boundary problems, a novel updating algorithm for the DP arrangement is developed so that the position of DPs is not only rearranged but the DPs are also reassigned the role of being on the boundary or not. The proposed method achieved reasonable results in numerical experiments for well-known moving boundary problems.