HYPERBOLIC CONSERVATION LAWS HAVING SOURCE TERMS AND DONOR CELL DIFFERENCING

Abstract

Modifications in the integration of the source terms in hyperbolic conservation laws such as those governing combustion, detonation and radiative transport, with a first order upwind differencing technique are proposed and analysed. The von Neuman stability and phase error analysis for a linear scalar equation, together with a few test problems is presented in order to compare the performance of the resulting variants of the donor cell scheme. It is established that when the source term is integrated using higher order formulae, the resulting scheme gives better resolution and has better stability limit and phase accuracy, compared to the standard single nodal value replacement. It is shown that integration by the trapezoidal rule gives sufficient accuracy and further improvement may not necessarily be achieved using better methods, such as the Simpson’s rule.