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Wienkers, Aaron F.
MPhil Project, University of Cambridge
Publication year: 2016

Abstract

The shearing box approximation to the compressible Euler equations modelling shearing, rotating, and stratified flows in a local frame is presented in a generalised form for eccentric discs. A semi-analytic solution describing the nonlinear laminar vertical resonant solutions to this model is found for the special case of an isothermal disc. The overall 2nd order finite volume method constructed and validated in Part I of this series is modified to solve for the oscillatory geometric source terms arising from the eccentric orbit. This modified algorithm based on the well-balanced MUSCL TVD scheme using the HLLC approximate Riemann solver is employed to solve for the 1D horizontally invariant laminar solutions first identified in Ogilvie (2001). The finite volume implementation is consequently validated against the known semi-analytic isothermal solutions for a range of disc eccentricities.

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