A fifth-order nonlinear spectral difference scheme for hyperbolic conservation laws. (15th May 2021) - Lin, Yu; Chen, Yaming; Deng, Xiaogang
Highlights: Nonlinear shock capturing interpolation scheme is developed for the spectral difference (SD) method using stencils within a single cell. The compactness of the original linear SD scheme is remained, keeping the advantage of the method in terms of parallel effciency. Abstract: We develop in this paper a fifth-order nonlinear spectral difference method for solving hyperbolic conservation laws, whose solutions often admit discontinuities. To avoid instability caused by the Gibbs phenomenon arising from interpolation across discontinuities, a fifth-order nonlinear interpolation scheme is proposed within a single cell, keeping the compactness of the original linear spectral difference method. Some numerical results are also presented to demonstrate the accuracy and effectiveness of the proposed method.