A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstr...

We consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain Ω in R with a Cboundary Γ. Navier boundary conditions can be expressed in the form ω(v) = (2κ−α)v · τ and v ·n = 0 on Γ, where v is the velocity, ω(v) the vorticity, n a unit normal vector, τ a unit tangent vector, and α is in L∞(Γ). Such solutions have been considered in [2] and [3], and, i...

Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

In this paper, the spectral volume (SV) method is extended to solve the Navier-Stokes equations by treating the viscous terms with a mixed formulation named local Discontinuous Galerkin approach. The SV method combines two key ideas, which are the basis of the finite volume and the finite element methods, i.e., the physics of wave propagation accounted for by the use of a Riemann solver and hig...

We consider solutions to the incompressible Navier–Stokes equations on the periodic domain Ω = [0, 2π] with potential body forces. Let R ⊆ H(Ω) denote the set of all initial data that lead to regular solutions. Our main result is to construct a suitable Banach space S A such that the normalization map W : R → S A is continuous, and such that the normal form of the Navier–Stokes equations is a w...

A finite element method to solve the Reduced Navier-Stokes Prandtl (RNS/P) equations is described. These equations are an asymptotic simplification of the full Navier-Stokes equations, obtained when one dimension of the domain is of one order smaller than the others. These are therefore of particular interest to describe flows in channels or pipes of small diameter. A low order finite element d...

We investigate the stabilizing effect of convection in three-dimensional incompressible Euler and Navier-Stokes equations. The convection term is the main source of nonlinearity for these equations. It is often considered destabilizing although it conserves energy due to the incompressibility condition. In this paper, we show that the convection term together with the incompressibility conditio...

A computational procedure based on a divergence-free H(div) method is presented for the Stokes and Navier-Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding H(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the calculation....

This paper presents a technique to improve the velocity error in finite element solutions of the steady state Navier–Stokes equations. This technique is called pressure separation. It relies upon subtracting the gradient of an appropriate approximation of the pressure on both sides of the Navier–Stokes equations. With this, the finite element error estimate can be improved in the case of higher...