Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929575656685568 |
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| author | Mel'nyk, Taras Rohde, Christian |
| author_facet | Mel'nyk, Taras Rohde, Christian |
| contents | The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Robin-type boundary condition involving convective and diffusive fluxes is imposed on the lateral surface. The limit problem for vanishing diffusion and the cylinder shrinking to an interval is a nonlinear first-order conservation law. For a time span that allows for a classical solution of this limit problem corresponding uniform pointwise and energy estimates are proven. They provide precise model error estimates with respect to the small parameter that controls the double viscosity-geometric limit. In addition, other problems with more higher Péclet numbers are also considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains Mel'nyk, Taras Rohde, Christian Analysis of PDEs 76R50, 35K59, 35B40, 35B25 The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Robin-type boundary condition involving convective and diffusive fluxes is imposed on the lateral surface. The limit problem for vanishing diffusion and the cylinder shrinking to an interval is a nonlinear first-order conservation law. For a time span that allows for a classical solution of this limit problem corresponding uniform pointwise and energy estimates are proven. They provide precise model error estimates with respect to the small parameter that controls the double viscosity-geometric limit. In addition, other problems with more higher Péclet numbers are also considered. |
| title | Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains |
| topic | Analysis of PDEs 76R50, 35K59, 35B40, 35B25 |
| url | https://arxiv.org/abs/2404.07538 |