Numerical investigation of buoyancy-driven compressible laminar flow using new method preconditioned all-speed roe scheme

In this study, numerical simulation is performed with a focus on the application of new modified preconditioned all-speed Roe scheme to simulate natural convection flows. The new modified preconditioned all-speed Roe Scheme primarily utilizes the local flow parameters for calculation of the coefficients of numerator in dissipation term of the scheme instead of using the global cut-off Mach number strategy (which is advantageous for natural convection flows) and has been shown to have better accuracy than preconditioned Roe Scheme for Low Mach number flows. For the present simulation, the compressible governing equation in conservation form, new modified preconditioned all-speed Roe scheme and dual time stepping are employed. The validation of numerical algorithm is divided into two investigations a) natural convection flow within differentially heated enclosed square cavity and b) open-ended vertical channel asymmetrically heated for a wide range of Rayleigh number with air (Pr 0.72) as working fluid. Visualization of fluid flow dynamics conducted for both classes of geometries for all range of Rayleigh number show similar phenomena in accordance with previous literatures and compared data also show very good agreement with previous literatures. All results indicate that the new modified preconditioned all-speed Roe scheme is very much competent and accurate for simulation of buoyancy-induced compressible convection flows without relying on the correct prediction of global cut-off Mach number.