Journals
Resources
About Us
Open Access

Derivative-Based Finite-Volume MR-HWENO Scheme for Steady-State Problems

Derivative-Based Finite-Volume MR-HWENO Scheme for Steady-State Problems

Year:    2024

Author:    Jiayin Li, Chi-Wang Shu, Jianxian Qiu

Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 877–907

Abstract

In this paper, we further extend the derivative-based finite-volume multi-resolution Hermite weighted essentially non-oscillatory (MR-HWENO) scheme proposed in our previous article (Li, Shu and Qiu, J. Comput. Phys., 446:110653, 2021) to simulate the steady-state problem. When dealing with the steady-state problem, the process of updating and reconstructing the function values is similar to the previous scheme, but the treatment of the derivative values is changed. To be more specific, instead of evolving in time, in the sense of cell averages, the scheme uses the derivative at the current time step and the function at the next time step to reconstruct the derivative at the next time step by direct linear interpolation. There are two advantages for this approach: the first is its high efficiency, when handling the derivative, neither the update on time nor the calculation of nonlinear weights is required; in the meantime, the CFL number can still be taken up to 0.6 as in the original scheme; the second is its strong convergence, the corresponding average residual can quickly converge to machine accuracy, thus obtaining the desired steady-state solution. One- and two-dimensional numerical experiments are given to verify the high efficiency and strong convergence of the proposed MR-HWENO scheme for the steady-state problems.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0339

Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 877–907

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Finite-volume multi-resolution scheme HWENO scheme Runge-Kutta method steady-state problem.

Author Details

Jiayin Li

Chi-Wang Shu

Jianxian Qiu