The study of different discretized schemes for density and convection terms in high speed compressible flow using the pressure-based method

•CLEAR algorithm successfully predicts the compressible flows in present work.•SMART density scheme can accelerate the iteration convergence.•FUD density scheme is more stable than the other two density schemes.•OFCUI convection scheme cost the least time among the three convection schemes.•ADBQUCKEST convection scheme is more stable than the other two convection schemes.

The pressure-based method shows the potential to develop the procedure for the flow of entire spectrum of Mach numbers. In the paper the pressure-based CLEAR algorithm is adopted to compute the compressible flows. Meanwhile the performance of different schemes for density and convection terms in compressible flows is investigated. OFCUI, ADBQUICKEST and HLPA schemes are used to discretize the convection term. FUD scheme, the second-order center difference scheme blended first upwind scheme and SMART scheme are used to calculate the density. Flow in a converging–diverging nozzle and flow over a bump are taken as the test cases. Results show that CLEAR algorithm is reliable to compute the compressible flows. The convergence rate accelerates by using SMART scheme to interpolate the density. ADBQUICKEST convection scheme shows the superiority on stability compared with the other two convection schemes.