Upwind Compact Implicit and Explicit High-Order Finite Difference Schemes for Level Set Technique

Abstract

This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind, especially implicit schemes compared to ENO and WENO schemes. In addition, CPU time is reduced compared to these methods. Hence, the upwind high-order schemes are suggested as excellent alternatives for the previous schemes to calculate spatial derivatives in the level set equation.