Date of Award

2016

Document Type

Open Access Master's Thesis

Degree Name

Master of Science in Mathematical Sciences (MS)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Alexander Labovsky

Committee Member 1

Allan Struthers

Committee Member 2

Aleksandr Sergeyev

Abstract

We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied to the problems with very small viscosity/diffusion coefficients. This is achieved by combining the defect correction technique for increased spatial accuracy (and for resolving the issue of high convection-to-difusion ratio) with the deferred correction in time (which allows for the usage of the computationally attractive partitioned scheme, yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate) into the defect-deferred correction method (DDC). The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step.

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