Advancements In Finite Element Methods For Newtonian And Non-Newt
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Advancements In Finite Element Methods For Newtonian And Non-Newt
Clemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-NewtvinCtouíứn University, kjgalvi(íỉ'clemson.eduFollow this and additional works at: https://tigerprints.clemson.edu/all_dissettatìonsPart of the Applied Mathematics CommonsRecommended CitationGalvin, Keith, 'Advancements In Finite Element Methods Ikx Newtonian And Non Newtonun Flows* (2013). AllDiw/tM Advancements In Finite Element Methods For Newtonian And Non-Newtioni. 1136. https://tlgerprintsxieinson edu/all_dissertations/1136Ihi* DiMCfUtlon » brought to you far free and open XÍO) by the Dtaerutlons it llgcrPAdvancements In Finite Element Methods For Newtonian And Non-Newt
nnti. It he. been accepted for induicon in All DlMcrutMni. by an authorized administrator of Tiprrfttnbi For more information. please contact kokedcộĩClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-NewtversityIn Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Mathematical SciencesbyKeith .1. Galvin41487Accepted by:Dr. Hyesuk Lee, Committee ChairDr. Leo Rebholz, Co-ChairDr. Chris Cox Dr. Vincent ErvinAbstractThis dissertation studies two important problems in the mathema Advancements In Finite Element Methods For Newtonian And Non-Newttics of computational fluid dynamics. The first problem concerns the accurate and efficient simulation of incompressible, viscous Newtonian flows, desAdvancements In Finite Element Methods For Newtonian And Non-Newt
cribed by the Xavier Stokes equations. A direct numerical simulation of these types of flows is, in most cases, not computationally feasible. Hence, tClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-Newts on the defective boundary problem for non Newtonian flows. Non Newtonian flows are generally governed by mote complex modeling equations, and the lack of standard Dirichlet or Neumann boundary 'conditions further complicates these problems. We present two different numerical methods to solve t hes Advancements In Finite Element Methods For Newtonian And Non-Newte defective boundary problems for non-Newtonian flows, with application to both generalized-Newtonian and viscoelastic flow models.Chapter 3 studies aAdvancements In Finite Element Methods For Newtonian And Non-Newt
finite element method for the 31) Navier-Stokes equations in velocityvorticity-helicity formulation, which solves directly for velocity, vorticity, HClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-Newtlaw for conservation of mass) and vorticity (to enforce the mathematical law that div(curl)= (1). We prove unconditional stability of the velocity, and with the nse of a (consistent) penalty term on the difference between the computed vorticity and curl of the com pnted velocity, we are also able to Advancements In Finite Element Methods For Newtonian And Non-Newt prove unconditional stability of the vorticity in a weaker norm. Numerical experiments are given that confirm expected convergence rates, and test thAdvancements In Finite Element Methods For Newtonian And Non-Newt
e method on a bcnclmuưk problem.Chapter 1 focuses on one main issue from the method presented in Chapter 3. which is the question of appropriate (and Clemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-Newt a numerical scheme implementing this new Ixnmdary condition to evaluate its effectiveness in a numericaliihttps://khothuvien.cori!experiment.Chapter 5 derives a new, reduced order, multiscale deconvolution model. Multiscale deconvolution models are a type of huge eddy simulat ion models, which filt Advancements In Finite Element Methods For Newtonian And Non-Newter out small energy scales and model their effect on the large scales (which significantly reduces the amount of degrees of freedom necessary for simuAdvancements In Finite Element Methods For Newtonian And Non-Newt
lations). We present both an efficient and stable numerical method to approximate our new reduced order model, and evaluate its effectiveness on two 3Clemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-Newtective boundary condition problem is formulated as a constrained optimal control problem, where a flow balance is forced on the inflow and outflow boundaries using a Neumann control. The control problem is analyzed for an existence result and the Ijigrange multiplier rule. A decoupling solution algo Advancements In Finite Element Methods For Newtonian And Non-Newtrithm is presented and numerical experiments are provided to validate robust ness of the algorithm.Finally, this work concludes with Chapter 7, whichAdvancements In Finite Element Methods For Newtonian And Non-Newt
studies two numerical algorithms for viscoelastic fluid flows with defective boundary conditions, where only flow rates or mean pressures are prescribClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith Galv Advancements In Finite Element Methods For Newtonian And Non-Newty conditions of the flow equations which yield an optimal functional value. Two different approaches are considered in developing computational algorithms for the constrained optimization problem, and results of numerical experiments are presented to compare performance of the algorithms.iiiTable of Advancements In Finite Element Methods For Newtonian And Non-Newt ContentsClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith GalvClemson UniversityTigerPrintsAll DissertationsDissertations41487Advancements In Finite Element Methods For Newtonian And Non-Newtonian FlowsKeith GalvGọi ngay
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