An implicit characteristic-flux-averaging method for the Euler equations for real gases. (English) Zbl 0723.76053
Summary: A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Riemann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equations of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.
MSC:
| 76K05 | Hypersonic flows |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
Keywords:
implicit characteristic-flux-averaging method; unsteady Euler equations; real gas effects; internal energy; Riemann solver; flux-split algorithm; Jacobian matrices; eigenvectors; mesh-sequencing methodReferences:
| [1] | ’3D Euler calculations using characteristic flux extrapolation’, AIAA Paper 85-0119, 1985. |
| [2] | ’NSFLEX–a computer program for the solution of the compressible Navier-Stokes equations’, MBB/LKE 122/AERO/MT/778, 1987. |
| [3] | and ’High order solutions of the Euler equations by characteristic flux averaging,’ ICAS Paper 86-1.3.1, 1986. |
| [4] | ’Hypersonic three dimensional Navier-Stokes calculations for equilibrium gas’ , AIAA Paper 89-2183, 1989. |
| [5] | Glaister, J. Comput. Phys. 74 pp 382– (1988) |
| [6] | Colella, J. Comput. Phys. 59 pp 264– (1985) |
| [7] | Grossman, AIAA J. 27 pp 524– (1989) |
| [8] | ’Characteristic flux averaging approach to the solution of Euler’s equations’, VKI Lecture Series, Computational Fluid Dynamics, 1987-04, 1987. |
| [9] | and ’Three-dimensional unsteady Euler equations solution using flux vector splitting’, AIAA Paper 84-1552, 1984. |
| [10] | and ’Verification of an implicit relaxation method for steady and unsteady viscous and inviscid flow problems’, AGARD CP 437, 1988, pp. 15-1-15-33. |
| [11] | Tsangaris, Z. Angew. Math. Mech. 70 pp t664– (1990) |
| [12] | and ’Improved mesh sequencing method for the accelerated solution of the compressible Euler and Navier-Stokes Equations’, 17th ICAS Conf., Stockholm, 9-14 September, 1990. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
