Border mapping multi-resolution (BMMR) technique for incompressible projection-based particle methods

TL;DR

The paper introduces BMMR, a multi-resolution border mapping technique for particle methods that improves accuracy and stability by aligning background grid particles with actual particles at borders, verified through 2D free surface flow benchmarks.

Contribution

It presents a novel border mapping multi-resolution method that enhances particle distribution consistency and reduces interpolation errors in projection-based particle simulations.

Findings

Improved accuracy in particle distribution near borders.

Enhanced stability in pressure calculations.

Validated performance with benchmark 2D free surface flow tests.

Abstract

A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between sub-domains with a 2:1 resolution ratio so that a single resolution framework is adopted to near-border particles calculations. The novelty of the BMMR is that it obtains the background grid from the mapping of the actual particle distribution in the border and, as a result, the location of the particles in the background grid exactly matches the location of the actual particles. In this way, such technique aims to reduce the error from the interpolation of the physical quantities in the background grid and to avoid sudden changes in the particle distribution that may lead to unstable local pressure calculation. In the coarse side of the border, the refinement is made by a triangulation and by placing fictitious particles in the midpoints of the triangles. In the fine side of the border, the derefinement is made by defining a set of fine particles that result in a particle distribution that best resembles a coarse one. The accuracy and computational performance of the BMMR implemented in a moving particle semi-implicit (MPS) simulation system are verified by using benchmark test cases of 2D free surface flows.