Numerical Study for the Three-Dimensional Rayleigh–Taylor Instability through the TVD/AC Scheme and Parallel Computation

perturbation of the fluid interface has an exponential growth The Rayleigh–Taylor instability is a gravity driven instability of a contact surface between fluids of different densities. The growth of this instability is sensitive to numerical or physical mass diffusion. h(t) 5 h0e, (1.1) For this reason, high resolution of the contact discontinuity is particularly important. In this paper, we address this problem using a second-order TVD finite difference scheme with artificial compreswhre h is the amplitude at time t, h0 is the initial amplitude, sion. We describe our numerical simulations of the 3D Rayleigh– and n is the growth rate of the perturbation. The growth Taylor instability using this scheme. The numerical solutions are rate is a function of the density ratio, viscosity, surface compared to (a) the exact 2D solution in the linear regime and (b) tension, and boundary conditions [2]. numerical solutions using the TVD scheme and the front tracking As a second regime, the unstable mode becomes nonlinmethod. The computational program is used to study the evolution of a single bubble and 3D bubble merger, i.e., the nonlinear evoluear. It grows into bubbles of light fluid and spikes of heavy tion of a single mode and the process of nonlinear mode–mode fluid. The bubble motion in this regime was analyzed by interaction. Q 1996 Academic Press, Inc. Taylor who gave the scaling law