Multidimensional adaptive order GP-WENO via kernel-based reconstruction
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913214173806592 |
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| author | May, Ian Lee, Dongwook |
| author_facet | May, Ian 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 stencils and reconstruction. A kernel-based approach inspired by Gaussian process (GP) modeling is presented here. This approach allows the creation of a scheme of arbitrary order with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows 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, as well as an easy-to-implement effective limiter for positivity preservation, both of 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03823 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multidimensional adaptive order GP-WENO via kernel-based reconstruction May, Ian 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 stencils and reconstruction. A kernel-based approach inspired by Gaussian process (GP) modeling is presented here. This approach allows the creation of a scheme of arbitrary order with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows 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, as well as an easy-to-implement effective limiter for positivity preservation, both of 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. |
| title | Multidimensional adaptive order GP-WENO via kernel-based reconstruction |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2304.03823 |