SUMMARYThe paper describes a new approach to approximating the convection term found in typical steady-state transport equations. A polynomial-based discretization scheme is constructed around a technique called 'curvature compensation'; the resultant curvature-compensated convective transport approximation is essentially third-order accurate in regions of the solution domain where the concept of order is meaningful. In addition, in linear scalar transport problems it preserves the boundedness of solutions. Sharp changes in gradient in the dependent variable are handled particularly well. But above all, the scheme, when used in conjunction with an AD1 pentadiagonal solver, is easy to implement with relatively low computational cost, representing an effective algorithm for the simulation of multi-dimensional fluid flows. Two linear test problems, for the case of transport by pure convection, are employed in order to assess the merit of the method.

A rational basis for correlating turbulent burning velocities is shown to involve the product of the Karlovitz stretch factor and the Lewis number. A generalized expression is derived to show how flame stretch is related to the velocity field. A new dimensionless correlation of experimental values of turbulent burning velocities is presented. Dimensionless groups also are used in correlations of laminar and turbulent flame extinction stretch rates. A distribution function of stretch rates in turbulent flames, based on an earlier one of Yeung et al ., is proposed and the experimental data are well predicted by a theory based on flamelet extinction by flame stretch with this distribution. Uncertainties arise concerning the role of negative stretch rate. Laminar flamelet modelling of complex combustion appears to have a broader validity than might be expected and some explanation for this is offered.

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SUMMARYThe paper describes and compares two different approaches to solving the equations of motion for fluid flow in a three-dimensional lid-driven cavity, when a higher-order approximation to convective transport is employed. One is based on the traditional pressure correction approach in conjunction with a pentadiagonal AD1 solver; the other follows a new unsegregated variable and FAS multigrid methodology. The results generated by both approaches, for laminar flow conditions, at Reynolds numbers of 100 and loo0 are compared with each other and with corresponding solutions obtained with a well known low-order approximation to convection. Cross-reference is also made to flow in a two-dimensional cavity at the same Reynolds numbers.KEY WORDS Unsegregated Multigrid High-order Finite-difference