An approximate Riemann solver for real gas parabolized NavierStokes equations
Under specific assumptions, parabolized NavierStokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized NavierStokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roes Riemann solver is developed as the core of a Godunov type finite volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roes Riemann solver for the parabolized NavierStokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.
riemann solver parabolized navier stokes equations real fluids