In this paper we propose the analysis of the incompressible nonhomogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of...

This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

This paper proposes and analyzes a stabilized finite-volume method FVM for the threedimensional stationary Navier-Stokes equations approximated by the lowest order finite element pairs. The method studies the new stabilized FVM with the relationship between the stabilized FEM FEM and the stabilized FVM under the assumption of the uniqueness condition. The results have three prominent features i...

Abstract We study the Stokes problem for incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral condition, Navier slip nonmonotone version Navier–Fujita and threshold leak condition frictional weak form leads to new class variational–hemivariational inequalities on convex sets velocity field. Solution existence compactness solution...

Introduction. The Collaborative Research Centre 747 “Micro cold forming” studies aspects of the production of micro components. Motivated by the engineering application of melting the end of thin wires by laser heating in order to accumulate material for a subsequent forming process, we study the melting and solidification of material with a free capillary melt surface. The model leads to a cou...

A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term u∇u. This perturbation is unbiased in that the expectation of a solution of the perturbed/quantized equation solves the determinis...

Using the fundamental solution of the heat equation, we give an expression of the solutions to two-dimensional initial-boundary value problems of the Navier-Stokes equations, where the vorticity is expressed in terms of a Poisson integral, a Newtonian potential, and a single layer potential. The density of the single layer potential is the solution to an integral equation of Volterra type along...

In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier–Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproble...

Strategies for choosing an eeective solver for a large sparse matrix equation are governed by the particular application. In this article, the context is the numerical solution of unsteady incompressible Navier-Stokes ow. When thousands of matrix equations diiering only in their right-hand sides must be solved, a multi-level one-way dissection scheme is an attractive choice. This method has the...