Study of capabilities of hybrid scheme for advection terms approximation in mathematical models of compressible flows

The hybrid method for approximation of advective terms is proposed in order to resolve flows in the wide Mach numbers region. This hybrid method is based on the Kurganov-Tadmor (KT) scheme and projection method PISO (Pressure Implicit with Splitting Operators). To construct this method Kurganov-Tadmor scheme for convective fluxes was formulated in implicit manner together with introduced blending function which switches between compressible regime (KT) and incompressible regime (PISO) depending on local characteristics of the flow. Such hybrid scheme gives next benefits: a) implicit treatment of diffusive terms allows to remove time step restrictions imposed by this kind of processes when approximated with explicit scheme; b) implicit formulation of convective terms together with mixing between PISO and KT produces better stability relied only on the flow Courant number, removing acoustic Courant number restrictions at low Mach number flows; c) however, acoustic flows can can also be reproduced - in this case, local acoustic Courant number must be decreased to values less the 1 in the whole computational domain; d) utilization of KT scheme as the basis for approximation of convection terms allows to achieve non-oscillating solution for both acoustic and compressible cases (Mach number larger then 0.3). In order to study hybrid method properties a set of cases with analytical solution or experimental data for different classes of flows was considered: a) compressible flows - propagation of the wave in straight channel (Sod's Problem), supersonic flow over flat wedge, supersonic flow over backward step, flow over forward step with supersonic velocities, flow in supersonic converging-diverging nozzle with shock wave; b) incompressible flows - subsonic flow of laminar viscous fluid in the channel with circle cross section, flow around cylinder in laminar and turbulent regimes, mixing of two gases in 2D flat channel; c) industrial and academic verification tests - superisonic flow of air in NASA nozzle for pressure ratio 5, expansion of stationary equilibrium hot plasma in vacuum; d) qualitative assessment of the hybrid method adequacy for industrial cases - numerical simulation of flows in high speed micro-compressor, simulation of two-phase flow in liquid ring pump. All materials are available for public access through GitHub project https://github.com/unicfdlab.