Contributions to the numerical solution of heterogeneous fluid mechanics models
A high order projection hybrid finite volume – finite element method is developed to solve incompressible and compressible low Mach number flows. Furthermore, turbulent regimes are also considered thanks to the k–ε model. The unidimensional advection-diffusion-reaction equation is used to construct,...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/16591 |
| Acceso en línea: | http://hdl.handle.net/10347/16591 |
| Access Level: | acceso abierto |
| Palabra clave: | Materias::Investigación::12 Matemáticas::1206 Análisis numérico::120613 Ecuaciones diferenciales en derivadas parciales Materias::Investigación::12 Matemáticas::1206 Análisis numérico::120608 Métodos interactivos |
| Sumario: | A high order projection hybrid finite volume – finite element method is developed to solve incompressible and compressible low Mach number flows. Furthermore, turbulent regimes are also considered thanks to the k–ε model. The unidimensional advection-diffusion-reaction equation is used to construct, analyze and assess high order finite volume schemes. Two families of methods are studied: Kolgan-type schemes and ADER methodology. A modification of the last one is proposed providing a new numerical method called Local ADER. The designed method is extended to solve the transport-diffusion stage of the three-dimensional projection method. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the schemes and to assess the performance of the method on several realistic test problems. |
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