Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach number flow and transonic flow regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes’ first problem) and a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm improves both the numerical accuracy and convergence efficiency and, thereby, ∗Aerospace Engineer, Member AIAA †Research Professor, Member AIAA ‡Senior Research Scientist, Associate Fellow AIAA This paper is declared a work of the U. S. Government and is not subject to copyright protection in the United States. enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.