Semi-Godunov schemes for general triangular systems of conservation laws

General m x m triangular systems of conservation laws in one space dimension are considered. These systems arise in applications like multi-phase flows in porous media and are non-strictly hyperbolic. Simple and efficient finite-volume schemes of the Godunov type are devised. These are based on a local decoupling of the system into a series of single conservation laws with discontinuous coefficients and are hence termed semi-Godunov schemes. These schemes are not based on the characteristic structure of the system. Some useful properties of the schemes are derived and several numerical experiments demonstrate their robustness and computational efficiency.