A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver

Abstract

A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver

Numerical Simulation of Steady-State Dump Combustor Operation With Auxiliary Fuel Injection

“…Similar accuracy is achieved for the secondary zones. We find similar agreement with the maximum streamfunction value and location given by the average of values reported by Zhang (1990), Ghia et (11. (1982), Schreiber and Keller (19831, and Vanka (1985) for the unit aspect ratio problem.…”

“…For the long cavity (A = 2) the secondary zone becomes very large at Re = I000 and by Re = 5000 it is very similar to that shown for the shear-driven cavity at Re = 5610 in Figure 3c. These doublecounter rotating recirculation zones have been reported in the literature (Gatski er al., 1982;Zhang, 1990). Quantitatively, the location and maximum streamfunction value for the shallow cavity (A = 2) agree with Zhang (1990) to within 4.4% at Re = 5000.…”

“…These doublecounter rotating recirculation zones have been reported in the literature (Gatski er al., 1982;Zhang, 1990). Quantitatively, the location and maximum streamfunction value for the shallow cavity (A = 2) agree with Zhang (1990) to within 4.4% at Re = 5000. This discrepancy decreases with the Reynolds number, reaching exact agreement at Re = 100.…”

“…First, there exists a large body of results with which we can compare fluid dynamics for completely incompressible flows on a domain similar to ours, the lid-driven cavity (Gatski et a/., 1982; Ghia et cil., 1982;Schreiber and Keller, 1983;Vanka, 1986;Zhang, 1990). We have performed numerous fluid flow calculations on the lid-driven cavity using grids identical to those used for the reacting shear-driven cavlty described earlier.…”

“…The flow in a unit aspect ratio cavity is thought to become unsteady somewhere around a Reynolds number of 5000 (Vanka, 1985). Zhang (1990) reported no instability in aspect ratio two calculations at Reynolds numbers of 5000. Hence, our A = 1 flow-field is certainly steady, while for cold-flow at A = 2 some degree of instability cannot be ruled out.…”