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.

Use of a pressure-weighted interpolation method for the solution of the incompressible navier-stokes equations on a nonstaggered grid system

Abstract: A detailed study of the pressure-weighted interpolation method (PWIM) using a non-staggered grid proposed by Rhie and Chow [7] was conducted. Its implementation in the SIMPLEC algorithm in order to obtain results independent of relaxation factor is described. A comparison of predicted results for two test cases, one a flow in a shear-driven cavity and the other a laminar contraction flow, was made using both staggered and nonstaggered grids. Both hybrid and QUICK differencing schemes were used. QUICK differencing with a nonstaggered grid yielded results in closest agreement with experimental and numerical data. It was also found that in regions of very rapidly varying pressure gradients, PWIM can predict physically unrealistic convective velocities

The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems

Abstract: In 1995 the two senior authors of the present paper introduced a new algorithm designed to replace the Taylor–Galerkin (or Lax–Wendroff) methods, used by them so far in the solution of compressible flow problems. The new algorithm was applicable to a wide variety of situations, including fully incompressible flows and shallow water equations, as well as supersonic and hypersonic situations, and has proved to be always at least as accurate as other algorithms currently used. The algorithm is based on the solution of conservation equations of fluid mechanics to avoid any possibility of spurious solutions that may otherwise result. The main aspect of the procedure is to split the equations into two parts, (1) a part that is a set of simple scalar equations of convective–diffusion type for which it is well known that the characteristic Galerkin procedure yields an optimal solution; and (2) the part where the equations are self-adjoint and therefore discretized optimally by the Galerkin procedure. It is possible to solve both the first and second parts of the system explicitly, retaining there the time step limitations of the Taylor–Galerkin procedure. But it is also possible to use semi-implicit processes where in the first part we use a much bigger time step generally governed by the Peclet number of the system while the second part is solved implicitly and is unconditionally stable. It turns out that the characteristic-based-split (CBS) process allows equal interpolation to be used for all system variables without difficulties when the incompressible or nearly incompressible stage is reached. It is hoped that the paper will help to make the algorithm more widely available and understood by the profession and that its advantages can be widely realised. Copyright © 1999 John Wiley & Sons, Ltd.

A Finite Element Variational Multiscale Method for the Navier-Stokes Equations

Abstract: This paper presents a variational multiscale method (VMS) for the incompressible Navier--Stokes equations which is defined by a large scale space LH for the velocity deformation tensor and a turbulent viscosity $ u_T$. The connection of this method to the standard formulation of a VMS is explained. The conditions on LH under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier--Stokes equations are studied. Numerical tests with the Smagorinsky large eddy simulation model for $ u_T$ are presented.