Beams Document 7303-v1

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Numerical simulations in complex geometry: from imaging to computing without CAD

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Rob Ainsworth
Updated by:
Rob Ainsworth
Document Created:
15 May 2019, 10:35
Contents Revised:
15 May 2019, 10:35
Metadata Revised:
28 Jun 2019, 16:56
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In applications such as subsurface/geomechanical sciences, additive manufacturing, advanced prototyping,or biomedical sciences, imaging techniques are now providing an unprecedented level of resolution. As an inevitable consequence, the level of geometric complexity of the shapes obtained with imaging/computer-graphics techniques is posing severe challenges to CAD tools. We present an alternative approach to the numerical simulation of problems involving complex geometry, in which the CAD geometry generation is bypassed in favor of a new breed of immersed/embedded boundary methods of finite element type.Embedded boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and/or complex design. Unfortunately, many embedded boundary methods are difficult to implement due to the need to perform complex cell cutting operations at boundaries, and the consequences that these operations may have on the overall condition number of the ensuing algebraic problems. We present a new, stable, and simple embedded boundary method, the shifted boundary method (SBM), which eliminates the need to perform cell cutting. Boundary conditions are imposed on a surrogate discrete boundary, lying on the interior of the true boundary interface. We then construct appropriate field extension operators, with the purpose of preserving accuracy when imposing the boundary conditions. The SBM method is proved to be stable and convergent for the Poisson and linear advection diffusion problems. We further demonstrate the SBM on large-scale incompressible flow problems, multiphase flow problems, solid mechanics problems, and complex flow in porous media.
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