EFFECT OF TIME MARCHING SCHEMES ON PREDICTIONS OF OSCILLATORY NATURAL CONVECTION IN FLUIDS OF LOW PRANDTL NUMBER

Abstract

A comparative study is presented of two time marching schemes for simulating oscillatory natural convection of low-Prandtl-number fluids in a square cavity. Fully implicit time marching, which is first-order accurate in time, is compared with the second-order-accurate, semi-implicit (Crank-Nicolson) scheme. Both methods are implemented in a control-volume-based finite difference formulation with the central difference scheme used for advection and diffusion terms. Calculations are compared in detail for Gr = 10⁷ and Pr = 0.00S, and results for Gr = 10⁶ and 3 × 10" are briefly summarized. While both time marching schemes predict oscillatory convection at Gr = 10⁷ using an 82 × 82 grid and dimensionless time steps [( Δtα/ L²)Pr√Gr[of 1/80, the flow structure and dynamic behavior predicted by the semi-implicit scheme are more complex than those predicted by the fully implicit scheme. Moreover, it is shown that the semi-implicit calculations are independent of time step while the fully implicit calculations are not.

Notes

Address correspondence to Patrick J. Prescott, Department of Mechanical Engineering, Pennsylvania State University, 137 Reber Building, University Park, PA 16802-1412, USA