High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

Fan, Chuan1; Wu, Kailiang1,2

2024-12-15

10.1016/j.jcp.2024.113435

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

This paper proposes high-order accurate, oscillation-eliminating, Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws, motivated by the oscillation-eliminating (OE) discontinuous Galerkin schemes recently proposed in [M. Peng, Z. Sun, and K. Wu, 2024 [30]]. The OE-HWENO schemes incorporate an OE procedure after each Runge-Kutta stage, by dampening the first-order moments of the HWENO solution to suppress spurious oscillations without any problem-dependent parameter. The OE procedure acts as a moment filter and is derived from the solution operator of a novel damping equation, which is exactly solved without any discretization. Thanks to this distinctive feature, the OE-HWENO method remains stable with a normal CFL number, even for strong shocks resulting in highly stiff damping terms. To ensure the essentially non-oscillatory property of the OE-HWENO method across problems with varying scales and wave speeds, we design a scale-invariant and evolution- invariant damping equation and propose a generic dimensionless transformation for HWENO reconstruction. The OE-HWENO method offers several notable advantages over existing HWENO methods. First, the OE procedure is highly efficient and straightforward to implement, requiring only simple multiplication of first-order moments by a damping factor. Furthermore, we rigorously prove that the OE procedure maintains the high-order accuracy and local compactness of the original HWENO schemes and demonstrate that it does not compromise the spectral properties via the approximate dispersion relation for smooth solutions. Notably, the proposed OE procedure is non-intrusive, enabling seamless integration as an independent module into existing HWENO codes. Finally, we rigorously analyze the bound-preserving (BP) property of the OE-HWENO method using the optimal cell average decomposition approach [S. Cui, S. Ding, and K. Wu, 2024 [8]], which relaxes the theoretical BP constraint for time step-size and reduces the number of decomposition points, thereby further enhancing efficiency. Extensive benchmarks validate the accuracy, efficiency, high resolution, and robustness of the OE-HWENO method.

Hyperbolic conservation laws Hermite WENO scheme Oscillation-eliminating (OE) procedure Bound-preserving High-order accuracy Moment filter

SCI

英语

第一 ; 通讯

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:001319789700001

ACADEMIC PRESS INC ELSEVIER SCIENCE

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518055, Peoples R China

Fan, Chuan,Wu, Kailiang. High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2024,519.

Fan, Chuan,&Wu, Kailiang.(2024).High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws.JOURNAL OF COMPUTATIONAL PHYSICS,519.

Fan, Chuan,et al."High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws".JOURNAL OF COMPUTATIONAL PHYSICS 519(2024).