High-Order Methods for Incompressible Fluid Flow

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

M. O. Deville is a professor of numerical fluid mechanics at the Ecole Polytechnique Federale de Lausanne in Switzerland P. F. Fischer is a research scientist in the Mathematics and Computer Science Division of Argonne National Laboratory Since 1967, E. H. Mund has published extensively in the areas of nuclear reactor physics and computation, radiation transport, and applied mathematics. Dr. Mund is also part-time professor of nuclear engineering at the Universite Catholique de Louvain