A flow solver for the Euler and Navier‐Stokes equations for multi‐phase flows with a stiffened gas equation of state

Abstract

PurposeThis paper aims to develop an efficient numerical method for simulating multicomponent flows by solving the system of conservative equations closed by a general two parameters equation of state.Design/methodology/approachA finite difference method for solving the two‐dimensional Euler or Navier‐Stokes equations for multicomponent flows in a general curvilinear coordinate system is developed. The system of conservative equations (mass, momentum and energy) is closed with a general two parameters equation of state (ρe=(p+γp∞)/(γ−1)), which, associated to a γ‐formulation, allows easy computation of multicomponent flows. In order to enforce the stability of the numerical scheme, the Roe's flux‐difference splitting is adopted for the numerical treatment of the inviscid fluxes. The method is adapted to treat also unsteady flows by implementing an explicit Euler scheme.FindingsThe method was applied to compute various configurations of flows, ranging from incompressible to compressible fluid, including cases of single component flows or multicomponent ones. Computations show that the use of primitive variables instead of conservative ones, especially at low Mach numbers, improves the iteration process when the resolution is performed with a relaxation procedure such as Gauss‐Seidel method. Simulations of compressible flows with a strong shock show the ability of the present method to capture shocks correctly even with the use of primitive variables. To complete numerical tests, flows involving two fluids with the presence of interactions between a shock and a discontinuity surface have been treated successfully. Also, a case of cavitating flow has been considered in this work.Originality/valueThe present method permits the simulation of a large variety of multicomponent complexes flows with an efficient numerical taking advantage of Roe's flux‐difference splitting in curvilinear coordinate system.