Abstract
This contribution proposes a 3D immersed boundary method, based on Cartesian grids, modified to improve the accuracy along the boundary and the efficiency during the resolution.
On the one hand, the embedded domain will be defined by its CAD boundary representation with NURBS or T-Splines, instead of using an approximated faceted representation. The exact boundary representation of the embedded domain allows overcoming the major drawback of existing immersed methods that is the inaccurate representation of the physical domain. A novel approach to perform the numerical integration taking into consideration the exact representation of the physical domain is
presented and its accuracy and performance evaluated using numerical tests.
On the other hand, and now from the analysis point of view, we propose to use a Nested Domain Decomposition (NDD) reordering technique. When a direct solver is used to solve a system of equations a previous reordering is usually used in order to improve the performance of the solver. Usually this reordering is obtained via an optimization process which not always obtains the best reordering for the system of equations. In our case, the NDD is based on the Cartesian grid structure, intimately related to the mesh topology, thus providing an optimal reordering. This reordering will
yield in a significant reduction of the computational cost associated to the resolution of the system of equations.
