A hybrid pressure-based solver for nonideal single-phase fluid flows at all speeds

This paper describes the implementation of a numerical solver that is capable of simulating compressible flows of nonideal single-phase fluids. The proposed method can be applied to arbitrary equations of state and is suitable for all Mach numbers. The pressure-based solver uses the operator-splitting technique and is based on the PISO/SIMPLE algorithm: the density, velocity, and temperature fields are predicted by solving the linearized versions of the balance equations using the convective fluxes from the previous iteration or time step. The overall mass continuity is ensured by solving the pressure equation derived from the continuity equation, the momentum equation, and the equation of state. Nonphysical oscillations of the numerical solution near discontinuities are damped using the Kurganov-Tadmor/Kurganov-Noelle-Petrova (KT/KNP) scheme for convective fluxes. The solver was validated using different test cases, where analytical and/or numerical solutions are present or can be derived: (1) A convergent-divergent nozzle with three different operating conditions; (2) the Riemann problem for the Peng-Robinson equation of state; (3) the Riemann problem for the covolume equation of state; (4) the development of a laminar velocity profile in a circular pipe (also known as Poiseuille flow); (5) a laminar flow over a circular cylinder; (6) a subsonic flow over a backward-facing step at low Reynolds numbers; (7) a transonic flow over the RAE 2822 airfoil; and (8) a supersonic flow around a blunt cylinder-flare model. The spatial approximation order of the scheme is second order. The mesh convergence of the numerical solution was achieved for all cases. The accuracy order for highly compressible flows with discontinuities is close to first order and, for incompressible viscous flows, it is close to second order. The proposed solver is named rhoPimpleCentralFoam and is implemented in the open-source CFD library OpenFOAM((R)). For high speed flows, it shows a similar behavior as the KT/KNP schemes (implemented as rhoCentralFoam-solver, Int. J. Numer. Meth. Fluids 2010), and for flows with small Mach numbers, it behaves like solvers that are based on the PISO/SIMPLE algorithm.