Level set jet schemes for stiff advection equations: The semijet method

• An accurate and stable level set jet scheme is demonstrated.
• The accuracy exceeds the original semi-implicit level set method.
• The stability exceeds the original level set jet method.

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.