Monotone level-sets on arbitrary meshes without redistancing

TL;DR

This paper introduces smooth, monotone regularizations of the Heaviside function for level-set methods on arbitrary meshes and proposes four efficient alternatives to redistancing, enabling fully coupled two-fluid flow simulations with improved robustness and efficiency.

Contribution

It presents novel smooth, monotone regularizations of the Heaviside function and four approaches to avoid costly redistancing, advancing fully coupled level-set simulations.

Findings

New regularizations improve smoothness on non-uniform meshes.

Four redistancing alternatives reduce computational cost.

Benchmark tests demonstrate effectiveness of proposed methods.

Abstract

In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary meshes. We show that the regularized Heaviside function can be non-smooth on non-uniform meshes. Alternative regularizing definitions that are indeed smooth and monotonic, are introduced. These new definitions lead to smooth Heaviside functions by taking the changing local meshsize into account. The second issue is the computational cost and fragility caused by the necessity of redistancing the level-set field. In previous papers it is shown that strongly coupling the level-set convection with the flow solver provides robustness and potentially efficiency and accuracy advantages. The next step would be to include redistancing within the strong coupling part of the algorithm. The computational cost of current redistancing procedure prohibit this. Four alternative approaches for circumventing the expensive redistancing step are proposed. This should facilitate a fully coupled level-set approach. Some benchmark cases demonstrate the efficacy of the proposed approaches. These includes the standard test case of the vortex in a box. Based on these results the most favorable redistancing approach is selected.