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UBC Theses and Dissertations

Infrastructure for solving generic multiphysics problems Boivin, Charles


Numerical simulations of partial differential equations problems are used in a variety of domains. Such simulation tools allow the scientific community to solve problems of increasing complexity. This allows complete testing and simulation of a product or process even before it is created. The numerical simulation process can be separated into two main steps: domain preparation and numerical computation. The first step requires the scientist to define the domain on which the problem will be solved; it is then decomposed into a group of smaller regions. This domain division is called a mesh. The mesh is subsequently used by the solver to perform the numerical computations specific to the physical problem being solved. The accuracy of the solution obtained depends on the quality of the mesh and the physical description of the problem. As powerful and useful as they are, these numerical tools could be improved on two fronts. First, the time spent preparing a problem with a complex geometry for a simulation is sometimes very large and could be minimized by automation of the pre-processing steps. Second, numerical solvers are not used in all the problem domains where partial differential equation problems are encountered because of the difficulty in acquiring the numerical expertise needed to develop specialized solvers. The objective of this research was to make the numerical simulation process easier and more accessible to scientists by addressing these two problems. Specifically, a mesh generator capable of generating guaranteed-quality meshes for complex geometries with curved boundaries has been written. This program completely automates the meshing process, which results in a huge gain in domain preparation efficiency. Additionally, an existing numerical toolkit has been modified to allow multiphysics problems to be solved in a generic fashion. With this solver, scientists can simply describe the physics of a problem — as well as the interactions between the different physical phenomena — and a numerical solution can be obtained within days. High-quality meshes and results from multiphysics problems are included to demonstrate the effectiveness of the current research. Finally, future improvements to the efficiency and accuracy of the solver are discussed.

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