Time Step Validation Method Research for Low-Prandtl Number Fluid Numerical Simulation

Abstract

The stability condition of Courant number and diffusion number is proved for an SGSD (stability guaranteed second-order difference) scheme by von Neumann method in implicit and explicit discretization of the one-dimensional convection and diffusion terms. Then, a series of numerical simulations of fluid flow and heat transfer based on two-dimensional unsteady state model is used to study the combined natural and MHD (magnetohydrodynamics) convection in a Joule-heated cavity using the finite volume methods, for the fluid of Pr = 0.01, also we use an SGSD scheme and IDEAL (inner doubly iterative efficient algorithm for linked equations) algorithm. It is found that periodic oscillation flow evolves.We propose a new convergence concept for the simulation oscillation results; the results of the numerical experiments are presented and they confirm our theoretical conclusions. The convergence result is checked in another way. It is found that the two approaches have the same results and can judge the validity of the time step. The proposed method is helpful to get reliable results efficiently.