A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy ...

We review recent work on univariate prewavelets that are either spline prewavelets on non-equally spaced knots or prewavelets from spaces spanned by translates of radial basis functions with non-equally spaced centres. Some of the results on radial basis functions we present apply to more than one dimension as well, so long as the centres are again confined to a grid.