Parallel curved meshing for high-order finite element simulations

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Lu, Qiukai
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Electronic thesis
Mechanical engineering
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It is well known that high-order finite element methods (FEM) are among the most powerful methods for simulating complex engineering problems in terms of solution accuracy and rate of convergence. In order to fully realize the benefits of using high-order methods, the mesh entities representing curved domain geometry must be curved and provide high-enough order of geometry approximation to prevent the loss of convergence due to geometric approximation errors. For high-order finite element methods, it has been demonstrated that properly curved meshes with higher-order continuity between the elements representing curved domain can achieve better solution properties. Although attaining greater than C⁰ continuity is being increasingly used with tensor product representations over quadrilaterals, there is the desire to have higher than inter-element continuity on unstructured meshes where triangular finite element faces are used to represent curved domain surfaces.
This thesis presents developments of curved meshing procedures that effectively represent curved domain boundaries by using triangular surface patches of high accuracy and smoothness. A procedure has been developed to generate G¹-continuous triangular surface meshes based on positional and surface normal data sampled from the CAD model representing the problem domain. Specific parameterization approaches based on blending functions are used to define the mapping for curved element faces and volumes between local and global coordinate systems. To effectively adapt curved G¹ meshes to satisfy a desired mesh size field, a set of mesh modification operations, including topological as well as geometrical operations, have been extended to deal with the complexities risen from the high-order smooth mesh entities. The software implementation has been integrated with well established finite element solvers using high-order methods. Benefits of using adaptive curved meshing techniques are demonstrated through examples in the Computational Fluid Dynamics (CFD) applications for viscous flow analysis with curved boundary elements, as well as in Computational Electromagnetism simulations using vector finite elements.
May 2017
School of Engineering
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Rensselaer Polytechnic Institute, Troy, NY
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