The Segregated Approach to Predicting Viscous Compressible Fluid Flows

The SIMPLE method of Patankar and Spalding and its variants such as SIMPLER, SIMPLEC, and SIMPLEX are segregated methods for solving the discrete algebraic equations representing the equations of motion for an incompressible fluid flow. The present paper presents the extension of these methods to the solution of compressible fluid flows within the context of generalized segregated approach. To provide a framework for better understanding the segregated approach to solving viscous compressible fluid flows an interpretation of the role of pressure in the numerical method is presented. With this interpretation it becomes evident that the linearization of the equation for mass conservation and the approach used to solve the linearized algebraic equations representing the equations of motion are important in determining the performance of the numerical method. The relative performances of the various segregated methods are compared for several subsonic and supersonic compressible fluid flows.

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The Segregated Approach to Predicting Viscous Compressible Fluid Flows

Volume 1: Turbomachinery ◽

10.1115/86-gt-196 ◽

1986 ◽

Cited By ~ 20

Author(s):

J. P. van Doormaal ◽

G. D. Raithby ◽

B. H. McDonald

Keyword(s):

Numerical Method ◽

Compressible Fluid ◽

Equations Of Motion ◽

Fluid Flows ◽

Mass Conservation ◽

Viscous Compressible Fluid ◽

Algebraic Equations ◽

Simple Method ◽

Compressible Fluid Flows

The SIMPLE method of Patankar and Spalding and its variants such as SIMPLER, SIMPLEC and SIMPLEX are segregated methods for solving the discrete algebraic equations representing the equations of motion for an incompressible fluid flow. The present paper presents the extension of these methods to the solution of compressible fluid flows within the context of a generalized segregated approach. To provide a framework for better understanding the segregated approach to solving viscous compressible fluid flows an interpretation of the role of pressure in the numerical method is presented. With this interpretation it becomes evident that the linearization of the equation for mass conservation and the approach used to solve the linearized algebraic equations representing the equations of motion are important in determining the performance of the numerical method. The relative performance of the various segregated methods are compared for several subsonic and supersonic compressible fluid flows.

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III. On symmetric compressible fluid flows around a flat plate

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1965.0113 ◽

1965 ◽

Vol 285 (1402) ◽

pp. 413-422 ◽

Cited By ~ 2

Keyword(s):

Equation Of State ◽

Flat Plate ◽

Compressible Fluid ◽

Singular Integrals ◽

Stokes Equations ◽

Equations Of Motion ◽

Fluid Flows ◽

State Equation ◽

Ideal Gas ◽

Compressible Fluid Flows

The Navier-Stokes equations for compressible fluid flows around a semi-infinite flat plate under symmetric attack are investigated. It is shown that regular locally subsonic motions, which are defined by bounded pressures and temperature gradients at the edge, exist without placing any restrictions on, for instance, analytic fluid characteristics as equation of state, equation of viscosity, and so forth. Those regular motions are locally incompressible and, hence, display the same flow patterns around the leading or trailing edge of a plate as incompressible fluid motions. In contrast to the existence of regular solutions the equations of motion exclude any singular integrals for which the pressure is infinite at the edge of the plate, provided the equation of state and the equations for viscosity, conductivity and specific heat are sufficiently regular. In particular, no singular solution exists if, for instance, the ideal gas law, Sutherland’s formula of viscosity, etc., are prescribed.

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