In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open and traction boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For this type of problem, the project...

In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give superconvergent results, and thus will lead to overrefinement when served as a posteriori error estimator. This drawback is overcome by designing an immersed grad...

This paper presents a lowest-order immersed Raviart–Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve optimal convergence rates meshes, an (IFE) is constructed by modifying traditional element. Some important properties are derived including unisolvence IFE basis functions, approximation cap...

In this paper, thirdand fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To keep the compactness of the finite difference schemes and get global high order schemes, even at the interface where the wave number is discontinuous, the idea of the immersed interface method is employ...

From the immersed boundary (IB) method point of view, the solid part may mainly act as elastic body or rigid body. Traditionally, the IB approach for fluid and rigid body interaction or fluid dynamics with complex geometry and boundary conditions has been divided into two main categories: the feedback forcing approach and the direct forcing approach. In the direct-forcing IB approach, the body ...