Centred Unsplit Finite Volume Schemes For Multidimensional Hyperbolic Conservation Laws

New unsplit finite volume centred schemes are presented. The construction of the schemes relies on the finite-volume frame work suggested by Billett and Toro, and on two existent one-dimensional centred schemes, namely the FORCE and the SLIC schemes. First and second order accurate schemes are constructed. These are found to possess improved stability properties as compared to existent finite volume methods. An application to the two-dimensional shallow water equations shows that the proposed schemes are accurate, robust and efficient.