A dual-time method for two-dimensional unsteady incompressible flow calculations

Abstract

A method for computing unsteady incompressible viscous ows on moving or deforming meshes is described. It uses a well-established time-marching ÿnite-volume ow solver, developed for steady compressible ows past rigid bodies. Time-marching methods cannot be applied directly to incompressible ows because the governing equations are not hyperbolic. Such methods can be extended to steady incompressible ows using an artiÿcial compressibility scheme. A time-accurate scheme for unsteady incompressible ows is achieved by using an implicit real-time discretization and a dual-time approach, which uses a technique similar to the artiÿcial compressibility scheme. Results are presented for test cases on both ÿxed and deforming meshes. Experimental, numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved.

Modeling of fluid flow in a tube with a moving indentation

“…A moving mesh method for the computation of compressible viscous flow past deforming and moving aerofoils was developed by Gaitonde [6,7]. A sequence of body conforming grids and the corresponding grid speeds were required, where inner and outer boundaries of the grid moved independently.…”

Numerical Simulations of Flow and Fuel Regression Rate Coupling in Hybrid Rocket Motors

“…To maintain the monotonic character of the scheme we use the MINMOD type limiter applied to gradients in the regions where steep gradients and/or shocks are present. Due to the presence of the very strong source terms in the governing equations and in order to avoid the use of very small type steps, an implicit algorithm is used for time advancement and this is done using a dual time approach, [6]. The numerical simulation of the 1-D compressible flows coupled with the fuel regression rate law allows the calculation of the kinematic and thermodynamic variables throughout the flow field and fuel grain.…”

Validation with Numerical Simulations of a Simplified Model of a Hybrid Rocket Motor

“…The numerical solution procedure is based on the standard cell-centered finite volume scheme of Godunov type, coupled with an implicit second-order discretization in time [5,6]. The numerical fluxes at cells faces are evaluated using Roe's flux-difference scheme.…”