Work

Development of a Hermite-like weighted compact nonlinear scheme based on the two-stage fourth-order temporal accurate framework

Year: 2025

Type: article

Abstract: We develop in this work a ffth-order Hermite-like weighted compact nonlinear scheme (HWCNS) within the framework of a two-stage fourth-order Lax-Wendroﬀ type time discretization (Li and Du, 2016) based on the generalized Riemann problem (GRP) solver for hyperbolic conservation laws in this paper. While in the conventional WCNS, only the nodal values are solved, the HWCNS also evolves the midpoint values using a two-stage fourth-order temporal accurate scheme. The midpoint ﬂow variables and the nodal values are obtained using the information particularly provided by the GRP solver. The obtained midpoint values approximate the frst derivatives at the nodes. Then, a high-order nonlinear interpolation is proposed using the nodal values and their derivatives over a more compact stencil. There is no additional eﬀort to compute the frst derivative of the ﬂow variable as in the standard Hermite WENO or DG approach. Owing to itscompact stencils in space and time, this new scheme has been demonstrated with high numerical resolutionthrough benchmark test cases.

Source: Physics of Fluids

DOI: 10.1063/5.0254448

Authors: Weihao Xie, Zhiwei He, GuangXue Wang, Huaibao Zhang

Institutions: Sun Yat-sen University, Institute of Applied Physics and Computational Mathematics, Institute of Physics

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G7055717454, G7780368853