Title: An adaptive time-stepping strategy for the implicit solution of steady transonic flow

Authors: Ugur Turk; Erhan Turan; Mehmet Orhan; Ali Ecder

Addresses: Department of Mechanical Engineering, Bogazici University, 34342, Istanbul, Turkey ' Department of Mechanical Engineering, Bogazici University, 34342, Istanbul, Turkey ' Department of Mechanical Engineering, Pamukkale University, 20070, Denizli, Turkey ' Department of Mechanical Engineering, Bogazici University, 34342, Istanbul, Turkey

Abstract: This study addresses a novel adaptive time stepping procedure, which leads to selection of larger time steps allowed by the physics of the problem under consideration. Information about the gradients of the flow variables can be regarded as an indicator for determining proper amount of time step, in which the system evolved. In this study, the signals from the pressure sensors, which act according to the pressure gradients, are chosen as a measure to determine the magnitude of the local CFL number. Thus, the aimed methodology for the selection of the local time step with the use of 'pressure sensor' introduces optimal time steps to the implicit solution method by accounting for the pressure gradient in the solution domain, such that sharp pressure gradients encourages small time steps and vice versa. To illustrate the effect of proposed procedure, Newton Krylov (NK), with implicit pseudo time stepping method, has been employed to solve the compressible Euler equations for steady transonic case by turning on the pressure switch. Numerical experiments show that the introduced adaptive time stepping procedure decreases the computation time and the number of iterations, effectively.

Keywords: adaptive time stepping; convergence acceleration; steady transonic flow; implicit methods; Newton Krylov methods; preconditioning; incomplete lower–upper; ILU preconditioners; pressure sensors; pseudo time stepping; CFL selection; Courant–Friedrichs–Lewy; computational fluid dynamics; CFD; pressure gradients; compressible Euler equations.

DOI: 10.1504/PCFD.2015.069575

Progress in Computational Fluid Dynamics, An International Journal, 2015 Vol.15 No.3, pp.135 - 143

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 26 May 2015 *

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