the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...

The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advecti...

A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two-dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source ...

Abstract. We are concerned with the convergence of Lax-Wendroff type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroff scheme proposed by Lax and Wendroff in 1960 and its two step versions–the Richtmyer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth flux functions, we prov...

this work reports the results of the application of the second-order maccormack method for numerical solution of‎ the conservative form of two-dimensional non-hydrostatic and fully compressible navier-stokes equations governing an inviscid and adiabatic atmosphere‎. various aspects of the computational approach such as discretization of the governing equations for the interior and boundary poin...

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency ...

We are concerned with the convergence of Lax-Wendroo type schemes with high resolution to the entropy solutions for conservation laws. These schemes include the original Lax-Wendroo scheme proposed by Lax and Wendroo in 1960 and its two step versions{the Richtmyer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth ux functions, we prove the convergen...

We present an explicit finite-difference scheme for direct simulation of the motion of solid particles in a fluid. The method is based on a second order MacCormack finite-difference solver for the flow, and Newton’s equations for the particles. The fluid is modeled with fully compressible mass and momentum balances; the technique is intended to be used at moderate particle Reynolds number. Seve...