An immersed interface method for the Navier-Stokes equations on irregular domains

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...

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...

The Immersed Interface Method forthe Navier–Stokes Equationswith Singular Forces

Peskin’s Immersed Boundary Method has been widely used for simulating many fluid mechanics and biology problems. One of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain. However, the Immersed Boundary Method is known to be first-order accurate and usually smears out the soluti...

A Fast Finite Difference Method for Solving Navier-stokes Equations on Irregular Domains

A fast finite difference method is proposed to solve the incompressible Navier-Stokes equations defined on a general domain. The method is based on the vorticity stream-function formulation and a fast Poisson solver defined on a general domain using the immersed interface method. The key to the new method is the fast Poisson solver for general domains and the interpolation scheme for the bounda...