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A numerical investigation of matrix-free implicit time-stepping methods for large CFD simulations. (English) Zbl 1390.76688

Summary: This paper is concerned with development and testing of advanced time-stepping methods for large unsteady CFD problems in the method of lines approach, where the semi-discretization in space is performed first. The performance of several time discretization methods is studied numerically with regards to computational efficiency, order of accuracy, and stability, as well as the ability to effectively treat stiff problems. We consider matrix-free implementations, a popular approach for time-stepping methods applied to large CFD applications due to its adherence to scalable matrix-vector operations and a small memory footprint. We compare explicit methods with matrix-free implementations of implicit, linearly-implicit, as well as Rosenbrock-Krylov methods. We show that Rosenbrock-Krylov methods are competitive with existing techniques excelling for a number of problem types and settings.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations

Software:

RODAS; MATLODE; SENSEI
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Full Text: DOI arXiv

References:

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