A level set two-way wave equation approach for Eulerian interface tracking

Abstract

We present a new approach to perform Eulerian level set interface tracking. It consists in advecting the level set function using a second-order two-way wave equation instead of the standard one-way wave advection equation. The resulting numerical schemes are simple to implement, more stable, and significantly less prone to dissipation errors than popular (e.g., WENO) discretizations of the one-way advection equation of higher order, in particular for long advection times. While both the two-way wave advection and the associated numerical schemes were derived previously, these approaches have never been combined with level set advection. Since the level set function to advect is smooth by construction, this ensures the stability of the solution when using the two-way advection equation discretized using centered finite difference schemes. Our numerical tests show that the two-way wave equation approach yields more accurate results than the standard one-way wave equation for the level set advection, at a considerably smaller computational cost.