2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

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...

Book review:
 MacCormack, Patricia. The Ahuman Manifesto: Activism for the End of Anthropocene. London: Bloomsbury Academic, 2020. 224 pages. ISBN 9781350081093. E-book. £15.83.

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

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...

This paper considers a deep analysis of three-level explicit time-split MacCormack method, namely the locally one-dimensional for numerical solution two-dimensional nonlinear evolutionary advection-diffusion equation subjects to suitable initial and boundary conditions. The splitting reduces computational cost algorithm. Under time-step restriction, both theoretical results on stability error e...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...