Related papers: Second order convergence of a modified MAC scheme …
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries…
In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the…
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…
A new method for interface tracking is presented. The interface representation, based on domain decomposition, provides the interface location explicitly, yet is Eulerian. This allows for well established finite difference methods on…
We study linear systems of equations arising from a stochastic Galerkin finite element discretization of saddle point problems with random data and its iterative solution. We consider the Stokes flow model with random viscosity described by…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
This paper is concerned with non-uniform fully-mixed FEMs for dynamic coupled Stokes-Darcy model with the well-known Beavers-Joseph-Saffman (BJS) interface condition. In particular, a decoupled algorithm with the lowest-order mixed…
Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous…
In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interface and reflect the interface condition in the variational…
A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…