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

Purpose – This 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/approach – A 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.Findings – The method was applied to compute various configurations of flows, ranging from incompressible to compressible fluid, inc...

[1]  Keh-Ming Shyue,et al.  An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems , 1998 .

[2]  Charles L. Merkle,et al.  Computation of low-speed flow with heat addition , 1987 .

[3]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[4]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[5]  K. H. Chen,et al.  Primitive variable, strongly implicit calculation procedure for viscous flows at all speeds , 1991 .

[6]  Yves Delannoy.  Modélisation d'écoulements instationnaires et cavitants , 1989 .

[7]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .

[8]  R. Abgrall.  How to Prevent Pressure Oscillations in Multicomponent Flow Calculations , 1996 .

[9]  J. Quirk.  A Contribution to the Great Riemann Solver Debate , 1994 .

[10]  B. Larrouturou.  How to preserve the mass fractions positivity when computing compressible multi-component flows , 1991 .

[11]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[12]  Richard Saurel,et al.  A Riemann Problem Based Method for the Resolution of Compressible Multimaterial Flows , 1997 .

[13]  T. Fransson,et al.  Experimental and Numerical Study of the Time-Dependent Pressure Response of a Shock Wave Oscillating in a Nozzle , 1995 .

[14]  APPLICATION OF AN IMPLICIT RELAXATION METHOD SOLVING THE EULER EQUATIONS FOR TIME-ACCURATE UNSTEADY PROBLEMS , 1990 .

[15]  U. Ghia,et al.  Study of incompressible flow separation using primitive variables , 1981 .

[16]  Eleuterio F. Toro,et al.  Numerical Computation of Two-Dimensional Unsteady Detonation Waves in High Energy Solids , 1979 .