In this work, the Characteristic-Based-Split (CBS) scheme is combined with the Minimum Polynomial Extrapolation (MPE) method to solve Navier-Stokes problems. We show the case of natural convection where the Navier--Stokes equations are coupled with the temperature equation. The local temperature difference induces a local density difference within the fluid and this produce the fluid motion. BU...

In this paper we address the existence, the asymptotic behavior and stability in L and L, 3 2 < p ≤ ∞, for solutions to the steady state 3D Navier-Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier-Stokes equations in L spaces, and we prove the stability of these soluti...

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least...

This paper is concerned with global solutions of the generalized Navier-Stokes equations. The generalized Navier-Stokes equations here refer to the equations obtained by replacing the Laplacian in the Navier-Stokes equations by the more general operator (−∆) with α > 0. It has previously been shown that any classical solution of the d-dimensional generalized NavierStokes equations with α ≥ 1 2 ...

We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as the skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes (RNS ) equations are defined on the boundary of the flow, and hence have reduced spatial dimensionality compared to the Navier-Stokes equations. This spatial reduction speeds up numer...

This paper is devoted to the study of a stationary problem consisting of the Boussinesq approximation of the Navier–Stokes equations and two convection–diffusion equations for the temperature and concentration, respectively. The equations are considered in 3D and a velocity–pressure formulation of the Navier–Stokes equations is used. The problem is complicated by nonstandard boundary conditions...

This paper describes a hybrid multicore/GPU solver for the incompressible Navier-Stokes equations with constant coefficients, discretized by the finite difference method. By applying the prediction-projection method, the Navier-Stokes equations are transformed into a combination of Helmholtzlike and Poisson equations for which we describe efficient solvers. As an extension of our previous paper...