Physical Sciences and Mathematics Commons^™

Immersed Boundary Smooth Extension (Ibse): A High-Order Method For Solving Incompressible Flows In Arbitrary Smooth Domains, David B. Stein, Robert D. Guy, Becca Thomases

Mathematics Sciences: Faculty Publications

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this …