An unconditionally stable, explicit Godunov scheme for systems of conservation laws

Common explicit, Godunov-type schemes are subject to a stability constraint. The time-line interpolation technique allows this constraint to be eliminated without having to make the scheme implicit or to linearize the equations. For 2 x 2 systems of conservation laws, a system of non-linear equations has to be solved in the general case to determine the left and right states of the Riemann problems at the cell inter-faces. However, if one cell in the domain is wide enough for the Courant number to be locally lower than unity, it is not necessary to solve a system anymore and the values at the next time step can be computed directly. The method is detailed for linear and non-linear scalar advection, as well as for 2 x 2 systems of hyperbolic conservation laws. It is illustrated by an application to a simplified model for two-phase flow in pipes, which is described using a 2 x 2 system of non-linear hyperbolic equations. Copyright (C) 2002 John Wiley Sons, Ltd.