Evaluation of a new scaling term in preconditioning schemes for computations of compressible cavitating and ventilated flows

This paper presents the application of a dual-time stepping scheme to the computation of unsteady cavitating and ventilated flows. The flows are modeled for multidimensional problems based on fully-compressible multi-component, multi-phase mixture Navier–Stokes equations. In order to handle the sharp discontinuity flows that previously developed preconditioning methods fail to do, the dual-time stepping scheme introduces a modified preconditioning parameter. This preconditioning parameter is defined using a “pressure-based” form so that accurate, efficient, and robust computations can be performed without dependence on the Mach number. The system of equations is solved on multi-block structured curvilinear grids with a high-resolution upwind scheme. Both the convergence performance and validation of the computational results are examined for various test cases including inviscid gaseous mixture flows in a tube, two-phase shock tube problem, free-surface flow in a nozzle, single-phase water flow, cavitating flows, transonic water flow, and ventilated flows over underwater vehicles. The results obtained with the modified form are in good agreement with the exact solutions and experimental data. In terms of accuracy, efficiency, and robustness, the modified form is strongly recommended for use in mixture flow computations when sharp discontinuities are present. •A numerical solution procedure for computations of unsteady cavitating and ventilated flows is presented.•A new scaling term in the dual-time stepping scheme is proposed.•Time accuracy of the dual-time stepping scheme is assessed.•The comparison of the numerical results with the experimental data shows a reasonably good agreement.