The Segregated Approach to Predicting Viscous Compressible Fluid Flows

Abstract

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.

Performance of an analogy-based all-speed procedure without any explicit damping

“…Hauke and Hughes (1993) have similarly worked in a ®nite-element context to develop their original compressible method to solve incompressible¯ows. Van Doormal et al (1987) have shown that a pressure-based method can be extended to solve compressible¯ows in a staggered grid arrangement. Karki and Patankar (1989) used a control-volume-based ®nite-difference method for a nonorthogonal coordinate system which suffers from sensitivity to grid smoothness.…”

“…Karki and Patankar (1989), Van Doormal et al (1987). Hence, they apply the incompressible primitive dependent variables, i.e.…”

“…Chen and Pletcher (1991) presented a collocated pressure-based technique for solving the time-dependent Navier±Stokes equations applicable to low Mach numbers. Karimian and Schneider (1995) used the approach of Van Doormal et al (1987) and developed a control-volume-based algorithm for a collocated grid arrangement.…”

Simulation of cooling of liquid Al–33wt.% Cu droplet impinging on a metallic substrate and its experimental validation

“…FLUENT 6.3.16 solves the above described equations using a control volume approach, which is fully implicit in time and uses upwind differencing in space [35]. A segregated solution algorithm [36] with a control volume based technique was used in the numerical method. The pressure and velocity were coupled with a semi-implicit method for pressure linked equation (SIMPLE) algorithm [37,38], which uses a guess-and-correct procedure for the calculation of pressure on the staggered grid arrangement.…”

Implementation of an efficient segregated algorithm-IDEAL on 3D collocated grid system

“…In 1984, Van Doormaal and Raithby proposed the SIMPLEC algorithm [7] , in which by changing the definition of the coefficients of the pressure-correction equation, the effects of dropping the neighboring grid velocity corrections (the second approximation in the SIMPLE algorithm) are partially compensated. Van Doormaal and Raithby also proposed the SIMPLEX algorithm [8,9] . In the SIMPLEX algorithm, by solving a set of algebraic equations for the coefficient d in the velocity-correction equation, the effects of dropping the velocity corrections of the neighboring grids are also taken into account to some degree.…”