Solution Verification Studies of a Pressure-Based Compressible Flow Solver

Abstract

Although considering the fluid to be incompressible is a common and valid approximation in most hydrodynamic simulations, certain phenomena like sloshing or slamming involve compressibility effects. In order to capture such effects, the maritime CFD code ReFRESCO is being extended with a compressible flow solver for the air in two-phase flow simulations. The compressible Navier-Stokes equations, discretized with a cell-centered, collocated finite volume method, are solved with a pressurebased SIMPLE algorithm that is compatible with the incompressible flow solver and enforces pressurevelocity-density coupling with a pressure-correction equation and an equation of state. In this paper, the compressible solver is tested for subsonic, transonic and supersonic flow of an inviscid perfect gas in a channel with an arc circular bump. We confirm that the pressure-based solver can indeed achieve iterative convergence to levels close to machine accuracy for all three regimes, with moderate decrease of convergence rate at higher Mach numbers and on finer grids. Grid refinement studies are performed to determine its accuracy and show observed orders of grid convergence between one and two for different quantities and different convection schemes, with lowest order for the supersonic regime, as expected. Finally, we notice that monotonic grid convergence can be attained if the grids are refined far beyond the levels typically reported in open literature.

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