four explicit finite difference schemes, including lax-friedrichs, nessyahu-tadmor, lax-wendroff and lax-wendroff with a nonlinear filter are applied to solve water hammer equations. the schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. the computational results are compared with those of the method of characteristics (moc), a...

In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly ahnost everywhere, will converge to weak solutions. The results are extensions of the classical Lax-Wendroff t...

The Lax-Wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities. The discrete operator, however, need not be derived from the divergence form of the continuous equations. Indeed, conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm ske...

We present a (partial) historical summary of the mathematical analysis finite difference and volume methods, paying special attention to Lax–Richtmyer Lax–Wendroff theorems. then state consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates recent generalization flux notion designed cope with general discrete functions.

Abstract. In this paper we introduce a definition of the local conservation property for numerical methods solving time dependent conservation laws, which generalizes the classical local conservation definition. The motivation of our definition is the Lax-Wendroff theorem, and thus we prove it for locally conservative numerical schemes per our definition in one and two space dimensions. Several...

Abstract — An upwind and a Lax-Wendroff scheme are introduced for the solution of a one dimensional non-local problem modelling Ohmic heating of Foods. The schemes are studied regarding their consistency, stability and the rate of convergence for the cases that the problem attains a global solution in time. A high resolution scheme is also introduced and it is shown that it is total-variation-s...