Gerald W. Recktenwald, James W. Ramsey, and Suhas V. Patanakar
Presented at the ASME Winter Annual Meeting, Forum on Unsteady Flow-1989, 10-15 December 1989, San Francisco, CA.
Appears in Numerical Heat Transfer American Society of Mechanical Engineers, FED-Vol. 83, pp. 29-31, P.H. Rothe, (ed.).
Simulation of turbulent flow and heat transfer with finite-element or finite-difference methods usually involves solution of additional equations for turbulence quantities. The most popular turbulence closure method is the k-epsilon model, which requires solution of two differential equations throughout the calculation domain. Use of a turbulence model allows simulation of flow situations of practical interest, yet implementation of a turbulence model results in slower convergence and potential loss of numerical stability
The remarks in this paper applicable to SIMPLE-based algorithms in which the equations for each velocity component, the continuity equation, and all other dependent field variables are solved in sequence. This is sometimes referred to as a segregated method because while computing the coefficients for any one variable, say the u velocity component, all other field variables are assumed to be constant. Segregation artificially decouples the dependent variables, and this requires under-relaxation, especially of the velocity and pressure equations. Simulation of turbulent flows with the k-epsilon model introduces two additional field variables that are strongly coupled to the velocity equations. Under-relaxation of the k and epsilon equations is necessary, and this slows convergence even further.
The recommendations discussed herein are a byproduct of the attempt to solve an unsteady, variable density, turbulent flow. The physical problem was the flow inside the cylinders of gas springs and reciprocating compressors (Recktenwald, 1989). The primary objective was to first obtain a reliable numerical solution, and only then enhance numerical efficiency. Toward this end, the SIMPLER algorithm (Patankar, 1980) was chosen. It should be noted that a variant of the SIMPLE algorithm called PISO (Issa, 1985) has been applied to the calculation of flows in piston-cylinder assemblies (Begleris and Gosman, 1987). It remains to be seen how our enhanced version of SIMPLER compares to PISO.