Computers & Fluids 

Abstract: A new k -ϵ eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed in this paper. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints; the positivity of normal Reynolds stresses and the Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (i) rotating homogeneous shear flows; (ii) boundary-free shear flows including a mixing layer, planar and round jets; (iii) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (iv) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k -ϵ eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k -ϵ eddy viscosity model.

Abstract: The finite element discretisation technique is used to effect a solution of the Navier- Stokes equations. Two methods of formulation are presented, and a comparison of the effeciency of the methods, associated with the solution of particular problems, is made. The first uses velocity and pressure as field variables and the second stream function and vorticity. It appears that, for contained flow problems the first formulation has some advantages over previous approaches using the finite elemental method[1,2].

Abstract: This paper deals with the extension of some upwind schemes to hyperbolic systems of conservation laws with source term. More precisely we give methods to get natural upwind discretizations of the source term when the flux is approximated by using flux-difference or flux-splitting techniques. In particular, the Q- schemes of Roe and van Leer and the flux-splitting techniques of Steger-Warming and Vijayasundaram are considered. Numerical results for a scalar advection equation with nonlinear source and for the one-dimensional shallow water equations are presented. In the last case we compare the different schemes proposed in terms of a conservation property. When this property does not hold, spurious numerical waves can appear which is the case for the centred discretization of the source term.

Abstract: An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes.

Abstract: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of a two-phase flow where the interface can merge/break and the flow can have a high Reynolds number. A distance function formulation of the level set method enables us to compute flows with large density ratios (1000/1) and flows that are surface tension driven, with no emotional involvement. Recent work has improved the accuracy of the distance function formulation and the accuracy of the advection scheme. We compute flows involving air bubbles and water drops, among others. We validate our code against experiments and theory.