To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091–3120] to convection diffusion equations, we propose a nonconventional high order finite volume weighted essentially nonoscillatory (WENO) scheme which can be proved maximum-principle-satisfying. Two-dimensional extensions are straightforwa...

An analogue technique for the approximate solution of the biharmonic equation is used to determine the viscous drag at Reynolds number approaching zero for cylinders falling symmetrically in a liquid between parallel walls. Results obtained show good agreement with numerical solutions, with results by direct experiment and with the work of other authors. Streamlines are obtained with a maximum ...

The standard discretization of the Stokes and Navier-Stokes équations in vorticity and stream function formulation by affine finite éléments is known for its bad convergence. We present here a modified discretization, we prove that the convergence is improved and we establish a priori error estimâtes. Résumé. Il est bien connu que la discrétisation usuelle des équations de Stokes et de Navier-S...

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

Frictionless flows with finite vorticity are usually made determinate by the imposition of boundary conditions specifying the distribution of vorticity ' at infinity '. No such boundary conditions are available in the case of flows with closed streamlines, and the velocity distributions in regions where viscous forces are small (the Reynolds number of the flow being assumed large) cannot be mad...

We study the two-dimensional (2D) stochastic Navier-Stokes (SNS) equations in the inertial limit of weak forcing and dissipation. The stationary measure is concentrated close to steady solutions of the 2D Euler equations. For such inertial flows, we prove that bifurcations in the flow topology occur either by changing the domain shape, the nonlinearity of the vorticity-stream-function relation,...

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [14] to convection diffusion equations, we propose a non-conventional high order finite volume weighted essentially non-oscillatory (WENO) scheme which can be proven maximum-principle-satisfying. Two-dimensional extensions are straightforward. We also show that the same idea can be used to construct hi...

The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman−Forchheimer−Darcy (or Brinkman−Hazen−Dupuit−Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function vorticity equations were solved numerically in spherical c...

A key feature of three-dimensional fluid turbulence is the stretching and realignment of vorticity by the action of the strain rate. It is shown in this paper, using the cumulant-generating function, that the cumulative vorticity stretching along a Lagrangian path in isotropic turbulence obeys a large deviation principle. As a result, the relevant statistics can be described by the vorticity st...