KFVM-WENO: A high-order accurate kernel-based finite volume method for compressible hydrodynamics
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| Format: | Preprint |
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2024
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| author | May, Ian C. T. Lee, Dongwook |
| author_facet | May, Ian C. T. Lee, Dongwook |
| contents | This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory reconstruction is achieved through an adaptive order weighted essentially non-oscillatory (WENO-AO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions (RBF) and Gaussian process (GP) modeling, which we call KFVM-WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple-yet-effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message passing interface (MPI) is also provided. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_16543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | KFVM-WENO: A high-order accurate kernel-based finite volume method for compressible hydrodynamics May, Ian C. T. Lee, Dongwook Numerical Analysis This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory reconstruction is achieved through an adaptive order weighted essentially non-oscillatory (WENO-AO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions (RBF) and Gaussian process (GP) modeling, which we call KFVM-WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple-yet-effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message passing interface (MPI) is also provided. |
| title | KFVM-WENO: A high-order accurate kernel-based finite volume method for compressible hydrodynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.16543 |