Date of Graduation

5-2020

Document Type

Thesis

Degree Name

Bachelor of Science

Degree Level

Undergraduate

Department

Mathematical Sciences

Advisor/Mentor

Kaman, Tulin

Committee Member/Reader

Brewer, Dennis

Committee Member/Second Reader

Spicer, Tom III

Committee Member/Third Reader

Sakon, Josh

Abstract

The Rayleigh-Taylor Instability (RTI) is an instability that occurs at the interface of a lighter density fluid pushing onto a higher density fluid in constant or time-dependent accelerations. The Richtmyer-Meshkov Instability (RMI) occurs when two fluids of different densities are separated by a perturbed interface that is accelerated impulsively, usually by a shock wave. When the shock wave is applied, the less dense fluid will penetrate the denser fluid, forming a characteristic bubble feature in the displacement of the fluid. The displacement will initially obey a linear growth model, but as time progresses, a nonlinear model is required. Numerical studies have been performed in the past to accurately approximate this nonlinear model. A techniques called front tracking has provided an enhanced resolution and zero numerical diffusion that is helpful with the sharp discontinuities of the fluid properties in simulations involving RTI and RMI. Weighted essentially non-oscillatory (WENO) finite difference schemes are used for accurate and precise results in both early and late time of fluid mixing simulations. In more traditional projects, WENO schemes utilized Lax-Friedrichs flux splitting. However, an alternative type of splitting developed by Gilbert Strang splits a two-dimensional problem into two one-dimensional problems that are easier and faster to solve. His splitting method was shown to achieve up to second-order accuracy. For this research, such a splitting method was derived for higher-order accuracy in three-dimensional problems. RTI simulations utilizing this newly derived model were used to incorporate front tracking technique, WENO, and operator splitting in a way that has not been done for a three-dimensional problem.

Keywords

RMI; RTI; Computational Fluid Dynamics; Strang Splitting

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