This paper presents a study of the behavior of several difference approximations for the incompressible Navier–Stokes equations as a function of the computational mesh resolution. In particular, the under-resolved case is considered. The methods considered include a Godunov projection method, a primitive variable ENO method, an upwind vorticity stream-function method, centered difference method...

We the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numeric...

Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements. Motivated by designed examples for superfluids, we consider the influence of a geometric potential on vortices for fluids with finite viscosity and show numer...

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier–Stokes equations. We propose an extension of Arakawa’s classical finite difference scheme for fluid flow in the vorticity-stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and v...

In this study we describe parallel iterative and direct solution strategies for viscous flow computation using domain decomposition. Both stream function vorticity and primitive variable formulations are considered. The basic ideas associated with the element-by-element approach and subdomain approach can also be extended to other cell or control-volume approximate formulations. Numerical resul...

In 2001, Bertalmio, et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is obtained by numerically approximating the steady state solution of the 2D NSE vorticity transport equation, and simultaneously solving the Poisson problem bet...

In 2001, Bertalmio, et. al. drew an analogy between the image intensity function for the image inpainting problem and the stream function in a two-dimensional (2D) incompressible fluid. An approximate solution to the inpainting problem is obtained by numerically approximating the steady state solution of the 2D NSE vorticity transport equation, and simultaneously solving the Poisson problem bet...

To cite this version: Abboud, Toufic and Salaün, Michel and Salmon, Stéphanie Coupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem. (2004) Numerical Methods for Partial Differential Equations, vol. 20 (n° 5). pp. 765-788. ISSN 0749159X Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulou...

A commonplace view of pressure-driven turbulence in pipes and channels is as “cascades” of streamwise momentum toward the viscous layer at the wall. We present in this paper an alternative picture of these flows as “inverse cascades” of spanwise vorticity, in the cross-stream direction but away from the viscous sublayer. We show that there is a constant spatial flux of spanwise vorticity, due t...

Deposition of silicon carbide (Sic) into two types of capillaries (1.5 mm dia. x 6 mm depth, 1.0 mm dia. x 4 mm depth) has been attempted by a vertical hot-wall-type chemical vapour infiltration (CVI) process using an SiCl4-CH4-H2 system. Dependence of the deposition temperature (Tdep) and the total gas pressure (Ptot) on the thickness distribution of Sic in the two types of the capillaries (pa...