Discretizations and Solvers for Coupling Stokes-Darcy Flows With Transport

This thesis studies a mathematical model, in which Stokes-Darcy flow system is coupled with a transport equation. The objective is to develop stable and convergent numerical schemes that could be used in environmental applications. Special attention is given to discretization methods that conserve mass locally. First, we present a global saddle point problem approach, which employs the discontinuous Galerkin method to discretize the Stokes equations and the mimetic finite difference method to discretize the Darcy equation. We show how the numerical scheme can be formulated on general polygonal (polyhedral in three dimensions) meshes if suitable operators mapping from degrees of freedom to functional spaces are constructed. The scheme is analyzed and error estimates are derived. A hybridization technique is used to solve the system effectively. We ran several numerical experiments to verify the theoretical convergence rates and depending on the mesh type we observed superconvergence of the computed solution in the Darcy region.Another approach that we use to deal with the flow equations is based on non-overlapping domain decomposition. Domain decomposition enables us to solve the coupled Stokes-Darcy flow problem in parallel by partitioning the computational domain into subdomains, upon which families of coupled local problems of lower complexity are formulated. The coupling of the subdomain problems is removed through an iterative procedure. We investigate the properties of this method and derive estimates for the condition number of the associated algebraic system. Results from computer tests supporting the convergence analysis of the method are provided. To discretize the transport equation we use the local discontinuous Galerkin (LDG) method, which can be thought as a discontinuous mixed finite element method, since it approximates both the concentration and the diffusive flux. We develop stability and convergence analysis for the concentration and the diffusive flux in the transport equation. The numerical error is a combination of the LDG discretization error and the error from the discretization of the Stokes-Darcy velocity. Several examples verifying the theory and illustrating the capabilities of the method are presented

Multiphysics simulation tools for designing motors for traction applications in hybrid and electric vehicles

Motor manufacturers are facing a difficult challenge in designing traction motors for the latest generation of hybrid and all-electric vehicles. The efficiency with which these motors can perform is critical, as it impacts on the vehicle range and battery life. Many of the issues involved in the motor design have a complex nature which requires multiple fields of physics such as electromagnetics (EM), mechanics and thermal analysis. All these physics are usually interdependent and have to be considered collectively in order to obtain optimal performance for a particular scenario. This paper presents a multiphysics simulation tool that was implemented to address this situation. The Opera FEA software suite [1] was developed to include a multiphysics analysis that can link several EM, thermal and stress analyses. Opera’s Machines Environment (parameterised template software for designing motors and generators) has been extended to allow easy setup of coupled multiphysics analyses such as EM to thermal and EM to stress. In order to further facilitate the coupling of different analyses, a link to the Python programming language was embedded in Opera FEA software. The embedded Python facility offers options to perform certain post-processing operations during the solving stage and hence allow data transfer between different stages of the multiphysics analysis. It also extends Opera’s capabilities to interact with other FEA software

Multiphysics simulation tools for designing motors for traction applications in hybrid and electric vehicles

Motor manufacturers are facing a difficult challenge in designing traction motors for the latest generation of hybrid and all-electric vehicles. The efficiency with which these motors can perform is critical, as it impacts on the vehicle range and battery life. Many of the issues involved in the motor design have a complex nature which requires multiple fields of physics such as electromagnetics (EM), mechanics and thermal analysis. All these physics are usually interdependent and have to be considered collectively in order to obtain optimal performance for a particular scenario. This paper presents a multiphysics simulation tool that was implemented to address this situation. The Opera FEA software suite [1] was developed to include a multiphysics analysis that can link several EM, thermal and stress analyses. Opera’s Machines Environment (parameterised template software for designing motors and generators) has been extended to allow easy setup of coupled multiphysics analyses such as EM to thermal and EM to stress. In order to further facilitate the coupling of different analyses, a link to the Python programming language was embedded in Opera FEA software. The embedded Python facility offers options to perform certain post-processing operations during the solving stage and hence allow data transfer between different stages of the multiphysics analysis. It also extends Opera’s capabilities to interact with other FEA software