An MPDATA-based solver for compressible flows

The theory of the high-resolution Multidimensional positive-definite advection transport algorithm (MPDATA) has been extensively developed since its invention in the early eighties. Many successful applications for geophysical flows followed. This paper introduces the original development of an MPDATA solver operating on a classical set of conservation laws, applicable to high-speed compressible flows. The solver belongs to a general class of the second-order nonoscillatory forward-in-Lime schemes. Theoretical considerations are supported with numerical examples. An elementary three-dimensional spherical wave-propagation problem illustrates that MPDATA correctly captures signal transfer in acoustic flows. Copyright (c) 2007 John Wiley & Sons, Ltd.