SUMMARYAlthough it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high-convection conditions, these methods continue to enjoy widespread popularity for numerical heat-transfer calculations, apparently owing to a perceived lack of viable high-accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular 'TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as this paper shows, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high-order accuracy, while requiring only a simple tridiagonal AD1 line-solver, as used in the majority of generalpurpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high-resolution nonoscillatory multidimensional steady-state high-speed convective modelling.

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

831) 439-6303Stringent wafer uniformity requirements demand thermal processing equipment in which wafers are subjected to identical processing conditions as much as possible. Conventional tube furnaces can suffer from end-to-end variations in gas composition in reacting ambients that can produce nonuniform f i l m properties. Novel gas injection systems that employ cross-wafer rather than axial gas flow paths can substantially improve wafer-to-wafer uniformity, provided that steps are taken to ensure even gas flow rates and chemical composition. Computational Fluid Dynamics (CFD) is often used for this purpose. CFD is an important tool to study, understand, and improve reactor designs, and allows prediction of wafer exposure conditions and on-wafer results early in the equipment design process. The use of CFD can greatly lower development costs and accelerate time-to-market.Three-dimensional CFD simulations have been used optimize hardware design and to predict gas flow uniformity and gas composition variations in thermal cross-flow reactors. The state-of-the-art multiphysics software package CFD-ACE+'" has been used for simulations of fully coupled. flow, heat transfer, and chemical reactions in an A1203 ALD process. Injector metering tube simulations show the decomposition of ozone in this pulsed-precursor deposition system and confirm adequate oxidant uniformity from end to end in the reactor. Three-dimensional simulations of candidate reactor designs quickly reveal improved reactor shapes and injector orientations that optimize cross-wafer gas flow uniformity. Simulations of ozone reactions in the reactor interior reveal spatial variations of atomic oxygen on the wafer surface in both static and rotating-wafer configurations, and demonstrate good oxidant Uniformity from the top to the bottom of the cross-flow reactor. 29 Outlet Holes 0 Concentration (mass Irac.) * " U R 2 N O 0 ,.a-* 185

Several workers have found evidence for the presence of longitudinal vortices in wind tunnel wall boundary layers near the centre line of each wall, although the only actual publication appears to be the reproduction of Bearman's work in Ref. 3. The phenomenon usually observed is shown in Fig. 1: the boundary layer is considerably thickened near the centre line. (This symmetrical and localised perturbation should be distinguished from the effect of non-uniformities in the wind tunnel screens which apparently also leads to longitudinal vortices, randomly spaced across the width of the working section). The hypothetical vortex pattern is also shown in Fig. 1: it arises because lateral pressure gradients in the wind tunnel contraction naturally deflect the slow-moving fluid in the boundary layer towards the centre line more strongly than the main ‘inviscid’ part of the flow, implying the generation of longitudinal vorticity: this is secondary flow of Prandtl's first kind.