An Expert System to Control the CFL Number of Implicit Upwind Methods

Vanderstraeten, Denis

doi:10.1007/978-1-4615-0663-8_91

Cited by 7 publications

(14 citation statements)

References 6 publications

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“…Currently, application-specific knowledge, intuition, and trial and error are still needed in order to determine appropriate values for the CFL control parameters. Using all CFL evolution strategies within an expert system like advocated in [39] may improve this situation.…”

Section: Discussionmentioning

confidence: 99%

“…A basic expert system is proposed in [39]. One can think of a complex expert system including all basic strategies, the ADL strategy, plausibility checks, a breakdown control, as well as repetitions of time steps or the use of multiple Newton steps.…”

Section: Discussionmentioning

confidence: 99%

“…increases the CFL number in a regular manner, also used, e.g., in [24,39]. The control parameters γ 0 and γ EXP completely determine a sequence of CFL numbers.…”

Section: Exponential Progression (Exp)mentioning

confidence: 99%

“…The Switched Evolution Relaxation (SER) [30] method often appears in the context of compressible flow, cf., e.g., [7,15,27,39]. The norm of the density residual, denoted by R k , is directly coupled with the CFL number of the following time step:…”

Section: Switched Evolution Relaxation (Ser)mentioning

confidence: 99%

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Iterative Solvers for Discretized Stationary Euler Equations

Pollul

Reusken

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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In this paper we treat subjects which are relevant in the context of iterative methods in implicit time integration for compressible flow simulations. We present a novel renumbering technique, some strategies for choosing the time step in the implicit time integration, and a novel implementation of a matrix-free evaluation for matrix-vector products. For the linearized compressible Euler equations, we present various comparative studies within the QUADFLOW package concerning preconditioning techniques, ordering methods, time stepping strategies, and different implementations of the matrix-vector product. The main goal is to improve efficiency and robustness of the iterative method used in the flow solver.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…increases the CFL number in a regular manner, also used, e.g., in [24,39]. The control parameters γ 0 and γ EXP completely determine a sequence of CFL numbers.…”

Section: Exponential Progression (Exp)mentioning

confidence: 99%

Section: Switched Evolution Relaxation (Ser)mentioning

confidence: 99%

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Iterative Solvers for Discretized Stationary Euler Equations

Pollul

Reusken

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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“…is used in many flow solvers [6,[22][23][24]. In every time step, the CFL number is increased by a constant factor i.…”

Section: Exponential Progression (Exp)mentioning

confidence: 99%

On CFL evolution strategies for implicit upwind methods in linearized Euler equations

Bücker

Pollul

Rasch

2008

Numerical Methods in Fluids

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SUMMARYIn implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a Courant-FriedrichsLevy (CFL) number in every iteration. A novel CFL evolution strategy is introduced and compared with two existing strategies. Numerical experiments using the adaptive multiscale finite volume solver QUADFLOW demonstrate that all three CFL evolution strategies have their advantages and disadvantages. A fourth strategy aiming at reducing the residual as much as possible in every time step is also examined. Using automatic differentiation, a sensitivity analysis investigating the influence of the CFL number on the residual is carried out confirming that, today, CFL control is still a difficult and open problem.

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