Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912643176988672 |
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| author | Boada, Angel Corbino, Johnny Dumett, Miguel Castillo, Jose |
| author_facet | Boada, Angel Corbino, Johnny Dumett, Miguel Castillo, Jose |
| contents | We investigate the construction and usage of mimetic operators in curvilinear staggered grids. Specifically, we extend the Corbino-Castillo operators so they can be utilized to solve problems in non-trivial geometries. We prove that the resulting curvilinear operators satisfy the discrete analog of the extended Gauss-Divergence theorem. In addition, we demonstrate energy and mass conservation in curvilinear coordinates for the acoustic wave equation. These findings are illustrated in two-dimensional and three-dimensional elliptic/hyperbolic equations and can be extended to other partial differential equations as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws Boada, Angel Corbino, Johnny Dumett, Miguel Castillo, Jose Analysis of PDEs Numerical Analysis 65M06 G.1.8 We investigate the construction and usage of mimetic operators in curvilinear staggered grids. Specifically, we extend the Corbino-Castillo operators so they can be utilized to solve problems in non-trivial geometries. We prove that the resulting curvilinear operators satisfy the discrete analog of the extended Gauss-Divergence theorem. In addition, we demonstrate energy and mass conservation in curvilinear coordinates for the acoustic wave equation. These findings are illustrated in two-dimensional and three-dimensional elliptic/hyperbolic equations and can be extended to other partial differential equations as well. |
| title | Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws |
| topic | Analysis of PDEs Numerical Analysis 65M06 G.1.8 |
| url | https://arxiv.org/abs/2407.01443 |