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A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids. (English) Zbl 0760.76070
Summary: A solution procedure for solving nonlinear time-marching problems is presented. The non-symmetric systems of equations arising from a Newton- type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High- speed flow computations demonstrate the effectiveness of these algorithms.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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