Steady nonlinear internal waves are commonly described by the Dubreil-JacotinLong equation. This equation contains unknown functions of the stream function, representing the density and vorticity fields. Often these are determined by upstream conditions where the flow is assumed to be known. But for the case when the waves are periodic in the horizontal direction, these functions need to be det...

We present a collection of methods for solving the incompressible Navier–Stokes equations in the plane that are based on a pure stream function formulation. The advantages of this approach are twofold: first, the velocity is automatically divergence free, and second, complicated (nonlocal) boundary conditions for the vorticity are avoided. The disadvantage is that the solution of a nonlinear fo...

The problem of determining the induced steady axially symmetric motion of an incompressible viscous fluid confined between two concentric spheres, with the outer sphere rotating with constant angular velocity and the inner sphere fixed, is numerically investigated for large Reynolds number. The governing Navier-Stokes equations expressed in terms of a stream function-vorticity formulation are r...

The dynamics of the two{dimensional turbulence is studied by a stochastic simulation method. The latter is based on a representation of the random vorticity eld and stream function by a multivariate stochastic process de-ned by a discrete master equation. It is demonstrated that in the continuum limit the complete hierarchy of coupled moment equations for the statistical formulation of the 2D N...

A numeriea! investigation for forced convection in a constant-temperaJure parallel pkue channel wilh porous cavity and block alternately emplaced on lhe bottom plaJe is presented in this work. The Brinkman-Forchheimer-extended Darcy mode~ whil:h accounts for the effects of impermeable boundary and inertia, is used to characterize the flow field inside the porous region. Solutions of Ihe coupled...

Spatio-temporal evolution of a small localized meander on a Gulf Stream-type baroclinically unstable jet over a topographic slope is investigated numerically using a threedimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent b...

The early history is presented of the prolific development of CFD methods in the Fluid Dynamics Group (T-3) at Los Alamos National Laboratory in the years from 1958 to the late 1960's. Many of the currently used numerical methods –PIC, MAC, vorticity-stream-function, ICE, ALE methods and the k-ε method for turbulence– originated during this time. The rest of the paper summarizes the current res...

The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions. The driven flow in a square cavity is used as the model problem. Solutions are obtained for configurations with Reynolds number as high as 10....

Tok tekutiny ostro lomeným potrubím v tvare V In this paper we study a viscous fluid flow over a V-shaped body for a range of Reynold's number from Re = 5 up to Re = 500. We solved the unsteady Naveir-stokes equations in the stream function vorticity formulation. The irregular physical domain is transformed into a rectangular shape using the elliptic grid generation. We applied the Finite difer...

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization...