A mimetic discretization of Westervelt's equation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910536599339008 |
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| author | Barham, William Morrison, Philip J. |
| author_facet | Barham, William Morrison, Philip J. |
| contents | A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which preserve the Hamiltonian structure in the dissipation-free limit, and which achieve the correct dissipation rate in the spatially-discrete dissipative dynamics. Moreover, by using spatial discretizations which preserve the de Rham cohomology, the non-evolving involution constraint for the vorticity may be exactly satisfied for all of time. Numerical examples are given using a mimetic finite difference spatial discretization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14718 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A mimetic discretization of Westervelt's equation Barham, William Morrison, Philip J. Numerical Analysis Mathematical Physics A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which preserve the Hamiltonian structure in the dissipation-free limit, and which achieve the correct dissipation rate in the spatially-discrete dissipative dynamics. Moreover, by using spatial discretizations which preserve the de Rham cohomology, the non-evolving involution constraint for the vorticity may be exactly satisfied for all of time. Numerical examples are given using a mimetic finite difference spatial discretization. |
| title | A mimetic discretization of Westervelt's equation |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2407.14718 |