The Burgers equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank Nicholson, used for solving the one-dimensional Burgers equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to the conve...

The rate of convergence of the Karhunen-Loeve expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers’ equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority o...

A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...

A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...

A case of combined planar Couette-Poiseuille flow corresponding to vanishing horizontal flux has been generalized by the introduction of a model for the surface velocity gradient. A relation corresponding to the Orr-Sommerfeld equation has been derived for this model. The critical value of the surface velocity gradient has been obtained. At the critical point, the corresponding critical Reynold...

sediment flushing of reservoirs is an operational technique, whereby previously accumulated sediments in the reservoirs are hydraulically removed by accelerated flow when the bottom desiltingoutlets of the dam are opened. in this research, the process of sediment flushing is simulated by a three dimensional numerical model in which sediment and flow interaction are reflected in the reservoirs. ...

A very simple proof is presented of the fact that the Orr-Sommerfeld equation for flows that approach exponentially to a constant at infinity has at most finitely many eigenvalues. A completely elementary argument shows that the Orr-Sommerfeld equation for such flows has no eigenvalues when the product of the Reynolds number and the wave number is small enough.

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for the case of low magnetic Reynolds number is obtained by integrating analytically the vorticity equation. Analysis of the resulted equation reveals a new ins...

We derive truncation error representation for the sixth order combined compact diierence (CCD) scheme for discretizing a one dimensional partial diierential equation. We also show that, for a model one dimensional convection diiusion equation, the CCD scheme produces numerical oscillatory solution, when the cell Reynolds number condition is violated. Numerical experiments are used to demonstrat...

We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the time-dependent Reynolds equation.