Reevaluating the boundary conditions of the perturbation pressure Poisson equation and an iterative solution on a non-uniform grid

dc.contributor.committeeChairDahl, Johannes M.L.
dc.contributor.committeeMemberAncell, Brian
dc.contributor.committeeMemberBruning, Eric
dc.creatorEspinoza, Roberto
dc.date.accessioned2021-09-14T19:39:03Z
dc.date.available2021-09-14T19:39:03Z
dc.date.created2021-08
dc.date.issued2021-08
dc.date.submittedAugust 2021
dc.date.updated2021-09-14T19:39:04Z
dc.description.abstractConvective scale numerical models have been used by many researches over the years to simulate supercellular storms and explore their features. One common technique is to relate these features to the structure of the pressure field, which is the solution to an elliptic partial differential equation known as a Poisson equation and often solved for numerically. The solution to such an equation is dependent on the boundary conditions prescribed to the pressure field. The goals of this thesis are two-fold. The first is to evaluate whether the condition applied to the bottom boundary should be modified by a “normal force,” similar to that acting on solid objects striking the surface. This development is aided by simulations of “cold bubbles,” regions of negative potential temperature perturbations, in George Bryan’s Cloud Model 1 (CM1). Secondly, an iterative method known as Jacobi’s Method is applied to the Poisson equation on an arbitrary grid which allows for stretching of grid points and higher model resolutions at select locations, such as near the surface. The method is tested on the well known problem of two infinite parallel plates and shown to converge to the exact analytical solution in a manner predicted by theory.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2346/87926
dc.language.isoeng
dc.rights.availabilityAccess is not restricted.
dc.subjectAtmospheric Science
dc.subjectMeteorology
dc.subjectPerturbation Pressure
dc.subjectPoisson Equation
dc.subjectJacobi's Method
dc.subjectJacobi Relaxation
dc.titleReevaluating the boundary conditions of the perturbation pressure Poisson equation and an iterative solution on a non-uniform grid
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentAtmospheric Science
thesis.degree.disciplineAtmospheric Science
thesis.degree.grantorTexas Tech University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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