Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method

TL;DR

The paper introduces the SemiJet method, combining semi-implicit schemes with level set jet techniques to efficiently and accurately handle stiff nonlinear advection problems involving high-order geometric quantities.

Contribution

It presents a novel SemiJet method that reduces smoothing steps and maintains high accuracy in stiff advection equations, improving upon previous level set approaches.

Findings

Requires only one smoothing step per update

Preserves high accuracy in stiff regimes

Avoids strict time step restrictions

Abstract

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.