Su Ziyao, Zhang Yan, Zhu Jun
In this paper, a new hybridization strategy for the sixth order unequal-sized weighted essentially non-oscillatory (HUS-WENO) scheme is designed for solving the nonlinear degenerate parabolic equations on structured meshes. This HUS-WENO scheme only uses the information defined on three unequal-sized stencils to obtain the optimal sixth order accuracy in smooth regions while maintaining stable, non-oscillatory and sharp discontinuity transitions. In addition, the linear weights in the proposed scheme are artificially set to be any random positive numbers with the only requirement that their sum equals one. To reduce CPU time, a hybridization strategy is designed based on the reconstruction polynomial of the six-point stencil in US-WENO scheme, which can accurately, efficiently, and automatically identify the troubled cells, and dose not contain any artificial parameters related to the problems. Finally, some numerical examples are used to verify the performance of the presented WENO scheme in various aspects, such as computational efficiency, low dissipation characteristics, shock capture ability, etc.
