Showing papers by "Eli Turkel published in 1996"

Preconditioning Methods for Low-Speed Flows.

Abstract: We consider the steady-state equations for a compressible fluid. For low-speed flow, the system is stiff because the ratio of the convective speed to the speed of sound is quite small. To overcome the difficulty, we alter the time evolution of the equations but retain the same steady-state analytic equations. To achieve high numerical resolution, we also alter the artifical viscosity of the numerical scheme, which is implemented conveniently by using other sets of variables in addition to the conservative variables. We investigate the effect of the artificial dissipation within this preconditioned system. We consider both the nonconservative and conservative formulations for artificial viscosity and examine their effect on the accuracy and convergence of the numerical solutions. The numerical results for viscous three-dimensional wing flows and two-dimensional multi-element airfoil flows indicate that efficient multigrid.

External flow computations using global boundary conditions

Abstract: We numerically integrate the compressible Navier-Stokes equations by means of a finite volume technique on the domain exterior to an airfoil. The curvilinear grid we use for discretization of the Navier-Stokes equations is obviously finite, it covers only a certain bounded region around the airfoil, consequently, we need to set some artificial boundary conditions at the external boundary of this region. The artificial boundary conditions we use here are non-local in space. They are constructed specifically for the case of steady-state solution. In constructing the artificial boundary conditions, we linearize the Navier-Stokes equations around the far-field solution and apply the difference potentials method. The resulting global conditions are implemented together with a pseudotime multigrid iteration procedure for achieving the steady state. The main goal of this paper is to describe the numerical procedure itself, therefore, we primarily emphasize the computation of artificial boundary conditions and the combined usage of these artificial boundary conditions and the original algorithm for integrating the Navier-Stokes equations. The underlying theory that justifies the proposed numerical techniques will accordingly be addressed more briefly.

On buffer layers as non-reflecting computational boundaries

Abstract: We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.