Effect of artificial speed of sound in ACM, EDACM, and EMV for two-dimensional cavity flow

This study compared various numerical schemes that have been reported with the assumption that artificial compressibility aids in the realization of explicit fluid dynamics simulations for a two-dimensional cavity flow. Four artificial compressible schemes, the artificial compressible method (ACM), entropically dumped ACM (EDACM), explicit method with virtual particles (EMV), were compared with a conventional incompressible scheme (simplified marker and cell, SMAC). The purpose of the comparisons is clarifying the validity of EMV in which the artificial speed of sound can be theoretically determined. In addition, the effect of the artificial speed of sound was investigated for ACM and compared with EMV. Moreover, three conditions of Reynolds numbers, Re=100, 1000, and 5000, were employed. Under steady-state conditions, the velocity and pressure distributions were found to be consistent among the EMV, ACM, EDACM, and SMAC. Further, the comparisons of the horizontal and vertical profiles indicated that these artificial compressible schemes reproduced the velocities using the incompressible scheme at three Reynolds numbers. In contrast, the temporal development of the velocity fields in the three artificial compressible schemes clearly exhibited small fluctuations in the velocity and pressure around the overall trends determined by SMAC. Further, the power spectral densities demonstrated that such fluctuations were due to compression-wave propagations with the artificial speed of sound. Although no clear differences were observed among EMV, ACM, and EDACM at these Reynolds numbers, EMV was determined to be advantageous in terms of theoretically determining the unique value of the artificial speed of sound once the lattice-grid system was fixed, whereas ACM and EDACM require sensitivity studies to select suitable values.