High-Order Oscillation-Eliminating Hermite WENO Method for Hyperbolic Conservation Laws
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914949472714752 |
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| author | Fan, Chuan Wu, Kailiang |
| author_facet | Fan, Chuan Wu, Kailiang |
| contents | This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The OE-HWENO schemes apply an OE procedure after each Runge--Kutta stage, dampening the first-order moments of the HWENO solution to suppress spurious oscillations without any problem-dependent parameters. This OE procedure acts as a filter, derived from the solution operator of a novel damping equation, solved exactly without discretization. As a result, the OE-HWENO method remains stable with a normal CFL number, even for strong shocks producing highly stiff damping terms. To ensure the method's non-oscillatory property across varying scales and wave speeds, we design a scale- and evolution-invariant damping equation and propose a dimensionless transformation for HWENO reconstruction. The OE-HWENO method offers several advantages over existing HWENO methods: the OE procedure is efficient and easy to implement, requiring only simple multiplication of first-order moments; it preserves high-order accuracy, local compactness, and spectral properties. The non-intrusive OE procedure can be integrated seamlessly into existing HWENO codes. Finally, we analyze the bound-preserving (BP) property using optimal cell average decomposition, relaxing the BP time step-size constraint and reducing decomposition points, improving efficiency. Extensive benchmarks validate the method's accuracy, efficiency, resolution, and robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-Order Oscillation-Eliminating Hermite WENO Method for Hyperbolic Conservation Laws Fan, Chuan Wu, Kailiang Numerical Analysis Computational Physics Fluid Dynamics This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The OE-HWENO schemes apply an OE procedure after each Runge--Kutta stage, dampening the first-order moments of the HWENO solution to suppress spurious oscillations without any problem-dependent parameters. This OE procedure acts as a filter, derived from the solution operator of a novel damping equation, solved exactly without discretization. As a result, the OE-HWENO method remains stable with a normal CFL number, even for strong shocks producing highly stiff damping terms. To ensure the method's non-oscillatory property across varying scales and wave speeds, we design a scale- and evolution-invariant damping equation and propose a dimensionless transformation for HWENO reconstruction. The OE-HWENO method offers several advantages over existing HWENO methods: the OE procedure is efficient and easy to implement, requiring only simple multiplication of first-order moments; it preserves high-order accuracy, local compactness, and spectral properties. The non-intrusive OE procedure can be integrated seamlessly into existing HWENO codes. Finally, we analyze the bound-preserving (BP) property using optimal cell average decomposition, relaxing the BP time step-size constraint and reducing decomposition points, improving efficiency. Extensive benchmarks validate the method's accuracy, efficiency, resolution, and robustness. |
| title | High-Order Oscillation-Eliminating Hermite WENO Method for Hyperbolic Conservation Laws |
| topic | Numerical Analysis Computational Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2409.09632 |