Reducing volume and shape errors in front tracking by divergence-preserving velocity interpolation and parabolic fit vertex positioning

TL;DR

This paper introduces divergence-preserving velocity interpolation and parabolic fit vertex positioning methods for front tracking, significantly improving volume and shape conservation during advection and remeshing in three-dimensional simulations.

Contribution

It presents novel divergence-preserving interpolation and parabolic fit vertex positioning techniques that enhance volume and shape accuracy in front tracking.

Findings

The divergence-preserving interpolation conserves volume and shape better than traditional methods.

The parabolic fit vertex positioning improves remeshing accuracy by an order of magnitude.

The proposed methods achieve high accuracy at lower computational costs.

Abstract

Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three-dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared in this work with other known interpolation methods in divergence-free and non-divergence-free test cases, with respect to volume conservation and shape preservation of the front. The presented interpolation method conserves the volume and shape up to an order of magnitude better than the conventionally used interpolation methods and is within the range of higher order interpolation methods at lower computational cost. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation by an order of magnitude compared to conventional remeshing algorithms.