A SEMI-LAGRANGIAN METHOD BASED ON WENO INTERPOLATION

Abstract

In this paper, a general Weighted Essentially NonOscillatory (WENO) interpolation is proposed and applied to a semi-Lagrangian method. The proposed method is based on the conservation law, and characteristic curves are used to complete the semi-Lagrangian method. Therefore, the proposed method satisfies conservation of mass and is free of the CFL condition which is a necessary condition for convergence.Using a several standard examples, the proposed method is compared with the third order Strong Stability Preserving (SSP) Runge-Kutta method to verify the high-order accuracy.

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