Development of fractional step methods for compressible flow solvers using variational multi-scale finite element formulations
(English) This thesis deals with finite element methods to solve compressible flow problems, an important branch of Computational Fluid Dynamics (CFD) whose applications are widespread in many areas of engineering and science. In spite of the increasing amount of computational resources made availab...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/690699 |
| Acceso en línea: | http://hdl.handle.net/10803/690699 https://dx.doi.org/10.5821/dissertation-2117-407226 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Enginyeria civil Àrees temàtiques de la UPC::Enginyeria mecànica Àrees temàtiques de la UPC::Matemàtiques i estadística 51 621 624 |
| Sumario: | (English) This thesis deals with finite element methods to solve compressible flow problems, an important branch of Computational Fluid Dynamics (CFD) whose applications are widespread in many areas of engineering and science. In spite of the increasing amount of computational resources made available for the scientific and engineering research communities, the numerical simulation of complex compressible phenomena in many practical applications is still a challenge. These type of flow problems are extremely demanding in what concerns numerical computations and memory requirements. In particular, in this thesis we investigate the possibility to solve the underlying algebraic systems in a decoupled manner, a technique usually called fractional step or segregation method. Although segregation techniques have been broadly studied and analyzed for the incompressible Navier-Stokes equations, allowing for the separate resolution of velocity and pressure unkonwns, much less has been explored for compressible problems. The interest on this type of technique not only comes from the fact that it permits a segregated calculation of the problem unkonwns (usually leading to better conditioned systems) but from the associated reduction of the computational cost. We study three different problems inside the compressible CFD research branch in separated chapters: the isentropic Navier-Stokes equations, the Navier-Stokes problem written in primitive variables (velocity, pressure and temperature), and the navier-Stokes problem written in the classical formulation with conservative variables (momentum, density, total energy). For each of these problems, first we propose a finite element stabilized formulation framed within the Variational MultiScale concept, which allows to use equal interpolation spaces for all the variables in play. Second, and once space and time discretizations are selected, we derive fractional step methods up to second order in time. Finally, all the schemes are implemented in a parallel multiphysics code and representative simulations are carried out in order to analyze the performance of the proposed techniques. |
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