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Appropriate spray modeling in multidimensional simulations of diesel engines is well known to affect the overall accuracy of the results. More and more accurate models are being developed to deal with drop dynamics, breakup, collisions, and vaporization/multiphase processes; the latter ones being the most computationally demanding. In fact, in parallel calculations, the droplets occupy a physical region of the in-cylinder domain, which is generally very different than the topology-driven finite-volume mesh decomposition. This makes the CPU decomposition of the spray cloud severely uneven when many CPUs are employed, yielding poor parallel performance of the spray computation. Furthermore, mesh-independent models such as collision calculations require checking of each possible droplet pair, which leads to a practically intractable O(np2/2) computational cost, np being the total number of droplets in the spray cloud, and additional overhead for parallel communications.

A one-dimensional, non-equilibrium, compressible law of the wall model is proposed to increase the accuracy of heat transfer predictions from computational fluid dynamics (CFD) simulations of internal combustion engine flows on engineering grids. Our 1D model solves the transient turbulent Navier-Stokes equations for mass, momentum, energy and turbulence under the thin-layer assumption, using a finite-difference spatial scheme and a high-order implicit time integration method. A new algebraic eddy-viscosity closure, derived from the Han-Reitz equilibrium law of the wall, with enhanced Prandtl number sensitivity and compressibility effects, was developed for optimal performance. Several eddy viscosity sub-models were tested for turbulence closure, including the two-equation k-epsilon and k-omega, which gave insufficient performance.