A parallelized Lattice-Gas solver for transient Navier–Stokes-flow: Implementation and simulation results

The last decade has seen the development of Lattice-Gas (LG) schemes as a complementary if not alternative method for the simulation of moderate Reynolds-Number Navier–Stokes flow. After a short theoretical introduction we present a detailed discussion of implementation features for a specific 2D-LG algorithm, which runs in parallel on a workstation-cluster, discuss simulation results and compare one of them to experimental studies. Finally, we attempt to point out present problems and perspectives of these methods.     

An efficient method of solving the Navier–Stokes equations for flow control

A new method of solving the Navier–Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen–Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier–Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier–Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier–Stokes equation. © 1998 John Wiley & Sons, Ltd.     

Turbulent transition simulation using the k–ω model

This paper describes a novel approach in simulating laminar to turbulent transition by using two-equation models. The Total Stresses Limitation (TSL) concept is used to make the two-equation model capable of predicting high-Reynolds-number transitional flow. In order to handle the transition triggered by laminar separation at a low Reynolds number location, which commonly occurs in high speed flow, a sensor is introduced to detect separation and trigger transition in the separated zone. Test cases include the classical flat-plate turbulent boundary flow, and low-pressure turbine cascade flows at design and off-design conditions. © 1998 John Wiley & Sons, Ltd.     

Stable and time-dissipative finite element methods for the incompressible Navier–Stokes equations in advection dominated flows

This paper examines a new Galerkin method with scaled bubble functions which replicates the exact artificial diffusion methods in the case of 1-D scalar advection–diffusion and that leads to non-oscillatory solutions as the streamline upwinding algorithms for 2-D scalar advection–diffusion and incompressible Navier–Stokes. This method retains the satisfaction of the Babuska–Brezzi condition and, thus, leads to optimal performance in the incompressible limit. This method, when, combined with the recently proposed linear unconditionally stable algorithms of Simo and Armero (1993), yields a method for solution of the incompressible Navier–Stokes equations ideal for either diffusive or advection-dominated flows. Examples from scalar advection–diffusion and the solution of the incompressible Navier–Stokes equations are presented.