Simulation of Rayleigh-Taylor Instability Suppression

Thomas Anderson, California Institute of Technology

It is well known that when two stratifed immiscible incompressible fluids are present in a horizontal channel of infinite extent, the Rayleigh-Taylor instability may occur. Namely, when a heavy fluid lies above a lighter fluid the system is known to be unstable. Recently efforts have focused on suppressing this instability with a transverse electric field. We consider the numerical solution of an asymptotic limit of this model. The resulting evolution equation we propose to solve is a PDE posed with periodic boundary conditions, but is highly nonlinear. More problematic is a nonlinear, nonlocal term in which the nonlocal operator is known solely through its Fourier transform. We develop a conservative, fully implicit numerical method using both classical finite differences and a novel pseudo spectral technique. Existing methods in the literature solving similar problems rely on the fortunate existence of integral representations of the nonlocal operators and exploit these representations by efficient quadrature methods. Instead, we present a fully general technique simultaneously compatible with explicit and implicit solvers alike. Due to our method's generality we are able to test our methods for correctness against multiple existing results. For efficiency due to the multiple time scales over which the interface evolves, we use temporal and spatial adaptivity. We also discuss preconditioning techniques and parallelization of the algorithm. We find numerical evidence of this stabilization and also compare it to simulations of the full fluid equations.

Abstract Author(s): Thomas Anderson, Peter Petropoulos