Boundary Algorithms for Multidimensional Inviscid Hyperbolic Flows

The advent of the computer has drastically changed and widened the field of applied mathematics. The "graphical and numerical methods" taught some thirty years ago rather incoherently in small courses have given way to a broad and complex treatment from very different view-points, and the struggle for ever-in-creasing accuracy has brought forth a considerable diver sification according to the different fields of application. The mathematical theorist, striving for general theorems and unified methods, might regret this development but as long as the demands of practical problems surpass what can be achieved by purely mathematical reasoning, the physicist and the engineer will also base their endeavours on physical grounds. In the wide field of fluid mechanics this development is marked by an in creasing number of conferences, lecture series and periodicals. It was felt, however, that the nature of the subject required a more extensive coverage of information than is possible in a ] 5 minute-8 pages paper, and that it was necessary, for instance, to give detailed reasoning, comparisons and even critical coding samples. Thus ultimately a monograph form of publication seemed desirable to back up the other channels and the idea of a specialized series was brought forth in the GAMM-Fachausschu~ for Numerical Methods in Fluid Mechanics. We are happy to have found in the Vieweg-Verlag a potent and understanding partner for this task and we hope for a lasting resonance both from readers and writers in this interesting field.