A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

作者：Rangarajan Ramsharan; Lew Adrian^*; Buscaglia Gustavo C

来源：Computer Methods in Applied Mechanics and Engineering, 2009, 198(17-20): 1513-1534.

DOI：10.1016/j.cma.2009.01.018

• Immersed boundary methods
• Elasticity
• Non-homogeneous boundary conditions
• Discontinuous Galerkin

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions.

• 出版日期2009