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One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows. These methods combine higher-order accuracy in smooth regions, with sharp, oscillation-free representation of embedded shocks, and are now known as "high-resolution schemes". This volume collects in one place many of the most significant papers in the development of high-resolution schemes as occurred at ICASE, together with introductions from the editors, written from the modern vantage point. Chapter I covers the early development of approximate Riemann solvers in the context of monotonic schemes. Chapter II continues with papers dealing with second-order total-variation-diminishing (TVD) schemes. Chapter III presents papers which show the historical development of total-variation-bounded (TVB) schemes at ICASE. Finally, Chapter IV collects papers on inherently multidimensional schemes, which preserve the attractive features of their one-dimensional predecessors.

Compressibility. --- Fluid dynamics --- Mathematical models. --- Physics. --- Thermodynamics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics, Simulation. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- High pressure physics --- Matter --- Pressure --- Properties --- Equations aux derivees partielles --- Onde de choc --- Volumes finis --- Methodes numeriques --- Differences finies