A Preconditioned Dual-Time, Diagonalized ADI Scheme for Unsteady Computations

The diagonalized ADI algorithm of Pulliam and Chaussee has been extended to include a timederivative preconditioning that permits efficient computation of flows over a wide range of Mach numbers. The algorithm has also been modified so that time-accurate analyses are possible through the use of dual-time stepping. The dual-time stepping has been incorporated in such a way that no additional factors are needed to handle the dual-time term in the left-hand-side inversion process. The preconditioning can accommodate general equations of state such as constant density (incompressible), perfect gas, or supercritical fluids. Unsteady vortex shedding from a circular cylinder is presented as an example of the capability of the algorithm.

[1]  D. Tritton.  Experiments on the flow past a circular cylinder at low Reynolds numbers , 1959, Journal of Fluid Mechanics.

[2]  T. Pulliam,et al.  A diagonal form of an implicit approximate-factorization algorithm , 1981 .

[3]  T. Pulliam.  Efficient solution methods for the Navier-Stokes equations , 1986 .

[4]  Charles Merkle,et al.  Time-accurate unsteady incompressible flow algorithms based on artificial compressibility , 1987 .

[5]  S. Weeratunga,et al.  A numerical method for Navier-Stokes equations with finite rate chemistry , 1989 .

[6]  S. Turns,et al.  Analysis of forced combusting jets , 1989 .

[7]  A. Jameson.  Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[8]  J. Shuen,et al.  A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds , 1992 .

[9]  T. Pulliam.  Time accuracy and the use of implicit methods. [in CFD , 1993 .

[10]  Meng-Sing Liou,et al.  Multigrid Time-Accurate Integrations of Navier-Stokes Equations , 1993 .

[11]  Jonathan Weiss,et al.  Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes , 1994 .

[12]  Charles L. Merkle,et al.  Effect of grid aspect ratio on convergence , 1994 .

[13]  C. Merkle,et al.  Dual time-stepping and preconditioning for unsteady computations , 1995 .

[14]  Charles E. Towne,et al.  Results and current status of the NPARC alliance validation effort , 1996 .