"Starting from the gas kinetic model, a new class of schemes for hyperbolic systems of conservation laws is presented. The flow solvers are based on the Boltzmann equations. The numerical discretization is based on the upwind cell vertex fluctuation-splitting model. The method is truly multidimensional in the sense that the splitting is independent of a particular normal direction; the geometry of the mesh does not influence the upwinding. Numerical results for inviscid flow test cases are presented to indicate the robustness and accuracy of the schemes. (C) 1998 John Wiley & Sons, Ltd."