Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.

High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations

Abstract: *† ‡ A high order multidomain spectral difference (SD) method is developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids. The method is easy to implement since it involves one-dimensional operations only, and does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube. The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy. In this paper, accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. High order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and the Couette flow. The capability of the method for more complex, inviscid and viscous flow problems with curved boundaries is also demonstrated.

Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part I: Light particles regime

Abstract: The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes equations. This system is intended to model the evolution of particles interacting with a fluid. The coupling arises from the force terms. The limit problem is the Navier-Stokes system with non constant density. The density which is involved in this system is the sum of the (constant) density of the fluid and of the macroscopic density of the particles. The proof relies on a relative entropy method.

Exact theory of three-dimensional flow separation. Part 1. Steady separation

Abstract: We derive an exact theory of three-dimensional steady separation and reattachment using nonlinear dynamical systems methods. Specifically, we obtain criteria for separation points and separation lines on fixed no-slip boundaries in compressible flows. These criteria imply that there are only four basic separation patterns with well-defined separation surfaces. We also derive a first-order prediction for the separation surface using wall-based quantities; we verify this prediction using flow models obtained from local expansions of the Navier–Stokes equations.

A hybridizable discontinuous Galerkin method for the compressible euler and Navier-Stokes equations

Abstract: In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the solution of the compressible Euler and Navier-Stokes equations. The method is devised by using the discontinuous Galerkin approximation with a special choice of the numerical fluxes and weakly imposing the continuity of the normal component of the numerical fluxes across the element interfaces. This allows the approximate conserved variables defining the discontinuous Galerkin solution to be locally condensed, thereby resulting in a reduced system which involves only the degrees of freedom of the approximate traces of the solution. The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties. In particular, we show that HDG produces optimal converges rates for both the conserved quantities as well as the viscous stresses and the heat fluxes. We present some numerical results to demonstrate the accuracy and convergence properties of the method.