Abstracts - KTH Mechanics

55
Development of a 3D transient incompressible Navier-Stokes solver
N. Suresh Kumar a, Anoop K. Dass a and Manmohan Pandey a
This work is concerned with the development of a 3D transient Navier-Stokes solver
through finite difference method. The solver is based on the fractional step method
proposed by Choi and Moin 1. The spatial discretization of the convective fluxes is carried
out through Kuwahara’s third order upwind scheme 2 and viscous fluxes through a fourth
order central difference scheme. In the fractional step method of Choi and Moin 1, every
time step is advanced in four substeps. The method requires the solution of pressure
Poisson equation in only one substep. In this method, continuity equation is satisfied only
at the final substep. In the present code, the pressure Poisson equation is solved through a
multigrid procedure with flexibility in choosing the number of levels to accelerate
convergence. As the code is third order accurate in space and second order accurate in time,
and multigrid accelerates its rate of convergence, it has DNS potential. However, the results
presented here are for the steady state laminar flow in a 3D cubical cavity for Re=1000 on a
129129129 staggered grid, which have been obtained through the code in a timemarching
fashion. Figure 1(a) shows the projection of streamlines on the cavity mid-plane
and Figure 1(b) compares the centreline x-velocity with those of Renwei et al. 3 and 2D
results produced on a 129129 grid. Our results compare well with those of Ref. 3 and
deviate from the 2D results, as expected.
a
Indian Institute of Technology Guwahati, Guwahati 781039, India
1
Choi and Moin, J. Comp. Physics, 113, 1 (1994)
2
Kawamura and Kuwahara, AIAA-85-0376 (1985)
3
Renwei et al., J. Comp. Physics, 161, 680 (2000)
(a)
Figure 1: (a) Projection of streamlines on the mid-plane, (b) Comparison of centreline xvelocity,
for Re=1000
(b)