The finite volume method on a Schwarzschild background
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915071538495488 |
|---|---|
| author | Dong, Shijie LeFloch, Philippe G. |
| author_facet | Dong, Shijie LeFloch, Philippe G. |
| contents | We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based on the finite volume methodology and takes the curved geometry into account. An interesting feature of our model is that no boundary conditions is required at the black hole horizon boundary. We establish that this scheme converges to an entropy weak solution to the initial value problem and, in turn, our analysis also provides us with a theory of existence and stability for a new class of conservation laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_10973 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The finite volume method on a Schwarzschild background Dong, Shijie LeFloch, Philippe G. Analysis of PDEs Numerical Analysis General Relativity and Quantum Cosmology 35L60, 65M05, 76L05 We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based on the finite volume methodology and takes the curved geometry into account. An interesting feature of our model is that no boundary conditions is required at the black hole horizon boundary. We establish that this scheme converges to an entropy weak solution to the initial value problem and, in turn, our analysis also provides us with a theory of existence and stability for a new class of conservation laws. |
| title | The finite volume method on a Schwarzschild background |
| topic | Analysis of PDEs Numerical Analysis General Relativity and Quantum Cosmology 35L60, 65M05, 76L05 |
| url | https://arxiv.org/abs/1901.10973 |