Error analysis of the immersed interface method for Stokes equations with an interface

An Immersed Interface Method for Incompressible Navier-Stokes Equations

An Immersed Interface Method for the Incompressible Navier--Stokes Equations with Discontinuous Viscosity Across the Interface

We present an immersed interface method for solving the incompressible Navier– Stokes equations with discontinuous viscosity across the interface and singular forces. The method is based on the augmented strategy proposed by Li, Ito, and Lai [Comput. Fluids, 36 (2007), pp. 622–635] to decouple the jump conditions of the fluid variables through the introduction of two augmented variables. In the...

An Immersed Interface Method for the Incompressible Navier-Stokes Equations in Irregular Domains

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pr...

Uniform Error Estimates for Navier-stokes Flow with a Moving Boundary Using the Immersed Interface Method

We prove that uniform accuracy of almost second order can be achieved with a finite difference method applied to Navier-Stokes flow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) near the interface using the immersed interface method, adding terms related to the jumps, on a regular gri...

A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

Submitted for the DFD08 Meeting of The American Physical Society A low-numerical dissipation immersed interface method for the compressible Navier-Stokes equations CARLOS PANTANO, KOSTAS KARAGIOZIS, RAMJI KAMAKOTI, University of Illinois at Urbana-Champaign — Immersed interface methods are an alternative methodology to unstructured methods for solving fluid dynamical problems around complex geo...