L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations

摘要

In this article an efficient sixth-order finite difference weighted essentially non-oscillatory scheme is developed to solve nonlinear degenerate parabolic equations. A new type of nonlinear weights are constructed with an introduction of a global smoothness indicator by a linear combination of local derivatives information involved in the smaller stencils that are developed with the help of generalized undivided differences in L1-norm. The advantage with these local smoothness indicators is that, each derivative involved in these are of higher order accurate as compared to the smoothness indicators developed by Liu et al. [SIAM, J. Sci. Comput, 2011]. Based on method of lines, we use strong stability preserving third-order Runge-Kutta (SSP-RK) scheme to evaluate time derivative. Various numerical tests are conducted in one and two dimensions to demonstrate the performance enhancement, resolution power and numerical accuracy of the scheme. The proposed scheme provides a better agreement in achieving the numerical solution as compared to the schemes developed by Liu et al. [SIAM, J. Sci. Comput., 2011] and Hajipour and Malek [Appl. Math. Model., 2012].