Interface problems have many applications. Mathematically, interface problems usually lead
to differential equations whose input data and solutions are non-smooth or discontinuous …

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in
complex geometries is presented. A boundary condition is enforced through a ghost cell …

Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

An open boundary algorithm for weakly compressible Smoothed particle hydrodynamics
(WCSPH) numerical models is presented. Open boundary conditions are implemented by …

In this paper a novel variable resolution method using particle splitting and coalescing for
the SPH numerical solution of the Navier–Stokes equations is presented. The key idea of the …

In the immersed interface method, boundaries are represented as singular force in the
Navier–Stokes equations, which enters a numerical scheme as jump conditions. Recently …

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase
flows, capable of handling large density and viscosity contrasts. The model is based on a …

An immersed boundary method for time-dependent, three-dimensional, incompressible
flows is presented in this paper. The incompressible Navier–Stokes equations are …

Immersed boundary methods and immersed interface methods are becoming increasingly
popular for the computation of unsteady flows around complex geometries using a Cartesian …

We present an efficient method for solving 2D incompressible viscous flows around multiple
moving objects. Our method employs an underlying regular Cartesian grid to solve the …