Level Set Jet Schemes for Stiff Advection Equations: The SemiJet Method
This work offers an incremental improvement for researchers using level set methods to simulate interfacial phenomena dominated by high-order geometric quantities.
The paper presents a semi-implicit level set jet scheme (SemiJet) for stiff advection equations, achieving improved efficiency by requiring only one smoothing step per update while maintaining accuracy and avoiding strict time step restrictions.
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.