Equilibrium Solutions for 2-Dimensional Non-axisymmetric Disks

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dc.contributor.advisorImamura, James
dc.contributor.authorSellers, Daniel
dc.date.accessioned2020-08-11T17:35:39Z
dc.date.available2020-08-11T17:35:39Z
dc.date.issued2020
dc.descriptionProject files include 1 page pdf.
dc.description.sponsorshipIn this study we seek equilibrium solutions for compressible, self-gravitating, 2-dimensional nonaxisymmetric disks. Such structures arise in binary star systems and other systems where tidal forces arise such as in the Earth-moon system. These disks are governed by a Scalar Momentum Equation (SME) and a partial differential equation describing hydrodynamic flow within the disk (Stream Function Equation). We solve these equations using a self-consistent field approach. At each iterative step, the Stream Function and gravitational potential are approximated at all grid points using Guass-Seidel iteration. These quantities, taken with the SME and appropriate boundary conditions are used to find an updated guess for the density distribution.
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dc.identifier.orcidNone
dc.identifier.urihttps://hdl.handle.net/1794/25520
dc.language.isoen_US
dc.publisherUniversity of Oregon
dc.rightsCreative Commons Guass-Seidel algorithms are applied to the relevant partial differential equations which have been discretized using a finite central-differencing technique. These solvers are implemented in python and verified using analytical solutions for simple cases, such as axisymmetric disks with uniform density. We find that our solvers converge to the analytical solutions over many iterations.
dc.subjectiterative solveren_US
dc.subjectnumerical solutionen_US
dc.subjectself-gravitating disken_US
dc.subjectPartial Differential Equationsen_US
dc.subjectGauss-Seidel Iterationen_US
dc.titleEquilibrium Solutions for 2-Dimensional Non-axisymmetric Disks
dc.typePresentation

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