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Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow

✍ Scribed by Hester Bijl; Mark H. Carpenter; Veer N. Vatsa; Christopher A. Kennedy

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
157 KB
Volume
179
Category
Article
ISSN
0021-9991

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✦ Synopsis

The accuracy and efficiency of several lower and higher order time integration schemes are investigated for engineering solution of the discretized unsteady compressible Navier-Stokes equations. Fully implicit methods tested are either the backward differentiation formulas (BDF) or stage-order two, explicit, singly diagonally implicit Runge-Kutta (ESDIRK) methods. For this comparison an unsteady twodimensional laminar flow problem is chosen: flow around a circular cylinder at Re = 1200. At temporal error tolerances consistent with engineering simulation, ⑀ ≈ 10 -1 -10 -2 , first-order implicit Euler (BDF1) is uncompetitive. While BDF3 is quite efficient, its lack of A-stability may be problematic in the presence of convection. At these same error tolerances, the fourth-order ESDIRK scheme is 2.5 times more efficient than BDF2. It is concluded that reliable integration is most efficiently provided by fourth-order Runge-Kutta methods for this problem where order reduction is not observed. Efficiency gains are more dramatic at smaller tolerances.

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