Numerical simulation of laminar mixing flow by develop of compressible algorithm

The use of the classical Boussinesq approximation is a straightforward strategy for taking into account the buoyancy effect in incompressible solvers. This strategy is highly effective if density variation is low. Whenever the density variation is high, this can cause considerable deviation from the correct prediction of fluid flow behavior and the accurate estimation of heat transfer rate. In this study, an incompressible algorithm is suitably extended to solve high-density-variation fields caused by strong natural-convection with mixing of oxygen and nitrogen in unsteady laminar compressible flow in a cavity. The continuity, momentum, energy and species equations are discritized based on finite volume methods and then numerically solved with extended algorithm with SIMPEL method. This new algorithm is capable of solving both Boussinesq and non-Boussinesq regimes. The fluid is assumed to be calorically an ideal gas and its thermodynamic properties depend on temperature and pressure. The extended algorithm is then verified by solving the benchmark convecting cavity problem at Rayleigh 106 and a temperature range of ε = 0.01–0.6. The results show that the method can vigorously solve unsteady mixing flow fields with extreme density variation.