Article history: Received 2 January 2014 Received in revised form 23 March 2014 Accepted 27 March 2014 Available online 2 April 2014

Embedded Boundary Methods (EBMs) [1] for the solution of Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems are typically formulated in the Eulerian setting, which makes them more attractive than Chimera and Arbitrary Lagrangian-Eulerian methods when the structure undergoes large structural motions and/or deformations. In the presence of viscous flows however, the...

We construct the cell-centered Finite Volume discretization of the twodimensional inviscid primitive equations in a domain with topography. To compute the numerical fluxes, the so-called Upwind Scheme (US) and the Central-Upwind Scheme (CUS) are introduced. For the time discretization, we use the classical 4th order RungeKutta method. We verify, with our numerical simulations, that the US (or C...

The cell-centered finite volume approximation of the Laplace equation in dimension one is considered. An exact expression of the error between the exact and numerical solutions is derived through the use of continuous and discrete Green functions. This allows to discuss convergence of the method in the L and L norms with respect to the choice of the control points in the cells and with respect ...

This paper presents an a posteriori residual error estimator for diffusion-convectionreaction problems approximated by some cell centered finite volume methods on isotropic or anisotropic meshes in Rd, d = 2 or 3. For that purpose we built a reconstructed approximation, which is an appropriate interpolant of the finite volume solution. The error is then the difference between the exact solution...

The article describes parallel multiphysics simulations of charged particles in microfluidic flows with the waLBerla framework. To this end, three physical effects are coupled: rigid body dynamics, fluid flow modelled by a lattice Boltzmann algorithm, and electric potentials represented by a finite volume discretisation. For solving the finite volume discretisation for the electrostatic forces,...

We develop a mixed finite element method for elliptic problems on hexahedral grids that reduces to cell-centered finite differences. The paper is an extension of our earlier paper for quadrilateral and simplicial grids [M. F. Wheeler and I. Yotov, SIAM J. Numer. Anal., 44 (2006), pp. 2082–2106]. The construction is motivated by the multipoint flux approximation method, and it is based on an enh...