Innovative Methods for Numerical Solution of Partial Differential Equations

This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry.

"A one-sided view" - the real story, B. van Leer; collocated upwind schemes for ideal MHD, K.G. Powell; the penultimate scheme for systems of conservation laws - finite difference ENO with Marquina's flux splitting, R.P. Fedkiw et al; a finite element based level-set method for multiphase flows, B. Engquist and A-K Tornberg; the GHOST fluid method for viscous flows, R.P. Fedkiw and X-D Liu; factorizable schemes for the equations of fluid flow, D. Sidilkover; evolution Galerkin methods as finite difference schemes, K.W. Morton; fluctuation distribution schemes on adjustable meshes for scalar hyperbolic equations, M.J. Baines; superconvergent lift estimates through adjoint error analysis, M.B. Giles and N.A. Pierce; somewhere between the Lax-Wendroff and Roe schemes for calculating multidimensional compressible flows, A. Lerat et al.; flux schemes for solving nonlinear systems of conservation laws, J.M. Ghidaglia; a Lax-Wendroff type theorem for residual schemes, R. Abgrall et al; kinetic schemes for solving Saint-Venant equations on unstructured grids, M.O. Bristeau and B. Perthame; nonlinear projection methods for multi-entropies Navier-Stokes systems, C. Berthon and F. Coquel; a hybrid fluctuation splitting scheme for two-dimensional compressible steady flows, P. De Palma et al; some recent developments in kinetic schemes based on least squares and entropy variables, S.M. Deshpande; difference approximation for scalar conservation law - consistency with entropy condition from the viewpoint of Oleinik's e-condition, H. Aiso; lessons learned from the blast wave computation using overset moving grids - grid motion improves the resolution, K. Fujii.