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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,... 

A new method of spatial filtering in high-order finite volume methods is presented and assessed. The base of this method is to filter face-averaged variables (fluxes) and then the recovery of cell-averaged ones. Two kinds of filtering method are proposed. The first kind is highly dissipative and appropriate for the numerical regions that need high dissipation, e.g. sponge zones. The second kind, on the other hand, is a precise method and hence is suitable for applying the high-order finite difference filters to the finite volume methods. Applying high-order finite difference filters directly to the high-order finite volume methods without using the proposed method causes stability problems...