Interface tracking using patches

TL;DR

This paper introduces a novel Eulerian interface tracking method using domain decomposition patches, enabling accurate, stable, and efficient simulations of complex fluid flows with explicit interface representation.

Contribution

The paper presents a new interface tracking approach based on domain decomposition that combines explicit interface location with Eulerian methods, suitable for complex fluid simulations.

Findings

Method achieves second order accuracy in interface position and curvature

Numerical results confirm convergence and mass conservation

Applicable to Stokes and Navier-Stokes flow simulations

Abstract

A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on uniform grids to be used for the numerics of advecting the interface and other computations. CFL-stable and second order accurate explicit and implicit time-stepping methods are derived. Numerical results are given to substantiate stated convergence properties, as well as convergence in interface curvature and mass conservation. Our method is applied to a boundary integral formulation for Stokes flow, and the resulting integrals are analyzed and treated numerically to second order accuracy. Finally, we embed our method in the familiar immersed boundary- and immersed interface methods for two-phase Navier-Stokes flow.