Meshless 2D Direct Numerical Simulation and heat transfer in a backward-facing step with heat conduction in the step

A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures. With this new procedure, preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this method lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, as well as in other formulations. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions. Preliminary calculations done in 2D laminar flows, suggest that the numerical diffusion and interpolation error are much important at low speeds, mainly when both, viscous and inertia forces are present. With this competitive and efficient procedure, the solution of the 2D Direct Numerical Simulation of turbulent flow with heat transfer on a backward-facing step is presented. The thermal energy is going to be transferred to the fluid through conduction on the step, with both constant temperature and heat flux conditions in the back wall of the step. The variation of the local Nusselt Number through the wall will be studied and its corresponding effect in the energy transfer to the fluid.