Pressure-based control-volume finite element method for flow at all speeds

We present a collocated pressure-based method for the solution of viscouslinviscid fluid flow problems incorporating compressible and incompressible regimes. The solution domain is discretized using a control-volume-based finite element method. The fully implicit method does not experience any stability difficulties due to compressibility effects at low Mach numbers. The pressure/velocity decoupling problem is fully resolved herein for flow regimes from incompressible through compressible flow. Transonic and supersonic flows are covered by including the pressure/density coupling, which arises in high-speed flows, in the continuity equation. This is done in such a manner that the continuity equation remains a constraint equation for pressure in all flow regimes. Test problems with wide variations in geometry and fluid physics have been successfully solved, demonstrating the generality and computational capability of the method. The scheme is both efficient and robust. The accuracy of the method has been checked by comparing the results with other numerical results available in the literature and with the exact solution.

[1]  N. Ron-Ho,et al.  A Multiple-Grid Scheme for Solving the Euler Equations , 1982 .

[2]  C. Rhie.  Pressure-based Navier-Stokes solver using the multigrid method , 1986 .

[3]  S. Patankar,et al.  Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations , 1988 .

[4]  Richard H. Pletcher,et al.  An implicit numerical scheme for the simulation of internal viscous flow on unstructured grids , 1994 .

[5]  Phillip Colella,et al.  Application of the Godunov method and its second-order extension to cascade flow modeling , 1983 .

[6]  Wei Shyy,et al.  Pressure-based multigrid algorithm for flow at all speeds , 1992 .

[7]  J. Peraire,et al.  Compressible and incompressible flow; an algorithm for all seasons , 1990 .

[8]  R. Pletcher,et al.  On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers , 1993 .

[9]  C. Merkle,et al.  Application of time-iterative schemes to incompressible flow , 1985 .

[10]  Charles L. Merkle,et al.  Time-derivative preconditioning for viscous flows , 1991 .

[11]  C. H. Liu,et al.  Preconditioned upwind methods to solve incompressible Navier-Stokes equations , 1992 .

[12]  Ali Turan,et al.  Evaluation of New Techniques for the Calculation of Internal Recirculating Flows , 1987 .

[13]  G. M. Johnson,et al.  Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm , 1983 .

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

[15]  S. M. H. Karimian,et al.  Advances in control-volume-based finite-element methods for compressible flows , 1994 .

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

[17]  O. C. Zienkiewicz,et al.  A general explicit or semi-explicit algorithm for compressible and incompressible flows , 1992 .

[18]  A. Roshko.  On the development of turbulent wakes from vortex streets , 1953 .

[19]  S. M. H. Karimian,et al.  Pressure-Based Computational Method for Compressible and Incompressible Flows , 1994 .

[20]  G. D. Raithby,et al.  The segregated approach to predicting viscous compressible fluid flows , 1986 .

[21]  G. Schneider,et al.  Numerical solution of two-dimensional incompressible Navier-Stokes equations - Treatment of velocity-pressure coupling , 1994 .

[22]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .