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.


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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