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A theme of linearization and approximate factorization provides the context for a retrospective overview of the development and evolution of implicit numerical methods for the compressible and incompressible Euler and Navier±Stokes algorithms. This topic was chosen for this special volume commemorating the recent retirements of R.M. Beam and R.F. Warming. A generalized treatment of approximate factorization schemes is given, based on an operator notation for the spatial approximation. The generalization focuses on the implicit structure of Euler and Navier±Stokes algorithms as nonlinear systems of partial dierential equations, with details of the spatial approximation left to operator de®nitions. This provides a uni®ed context for discussing noniterative and iterative time-linearized schemes, and Newton iteration for unsteady nonlinear schemes. The factorizations include alternating direction implicit, LU and line relaxation schemes with either upwind or centered spatial approximations for both compressible and incompressible ̄ows. The noniterative schemes are best suited for steady ̄ows, while the iterative schemes are well suited for either steady or unsteady ̄ows. This genera

Who reads An overview and generalization of implicit Navier–Stokes algorithms and approximate factorization?

Author

W.Roger Briley; Henry McDonald

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0045-7930)

Published

2001

Language

EN

Field

Engineering (Physical Sciences)