Related papers: Stable and convergent approximation of two-dimensi…
We prove in this paper the convergence of the Marker and cell (MAC) scheme for the dis-cretization of the steady-state and unsteady-state incompressible Navier-Stokes equations in primitive variables on non-uniform Cartesian grids, without…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We…
We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…
We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar function as it is common in level set based methods. Hence, the…
In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality between subgrid and…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We present a new collocated numerical scheme for the approximation of the Navier-Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity-pressure unknowns. This scheme is based on a recent scheme…
This paper presents stability and convergence analysis of a finite volume scheme (FVS) for solving aggregation, breakage and the combined processes by showing Lipschitz continuity of the numerical fluxes. It is shown that the FVS is second…
We present a (partial) historical summary of the mathematical analysis of finite differences and finite volumes methods, paying a special attention to the Lax-Richtmyer and Lax-Wendroff theorems. We then state a Lax-Wendroff consistency…
We present a novel stabilized isogeometric formulation for the Stokes problem, where the geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) patches, i.e., one patch on top of another in an arbitrary but…
We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 space dimensions. The equations are split into subsystems. The…
In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a…
In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final…
We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the…
We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…
The present paper is focused on the proof of the convergence of the discrete implicit Marker-and-Cell (MAC) scheme for time-dependent Navier--Stokes equations with variable density and variable viscosity. The problem is completed with…
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…
In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…
This paper develops a unified general framework for designing convergent finite difference and discontinuous Galerkin methods for approximating viscosity and regular solutions of fully nonlinear second order PDEs. Unlike the well-known…