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Comparative Assessment of Adaptive-Stencil Finite Difference Schemes for Hyperbolic Equations with Jump Discontinuities

Otis, Collin C. (2010) Comparative Assessment of Adaptive-Stencil Finite Difference Schemes for Hyperbolic Equations with Jump Discontinuities. Master's Thesis, University of Pittsburgh. (Unpublished)

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High-fidelity numerical solution of hyperbolic differential equations for functions with jump discontinuities presents a particular challenge. In general, fixed-stencil high-order numerical methods are unstable at discontinuities, resulting in exponential temporal growth of dispersive errors (Gibbs phenomena). Schemes utilizing adaptive stencils have shown to be effective in simultaneously providing high-order accuracy and long-time stability. In this Thesis, the elementary formulation of adaptive-stenciling is described in the finite difference context. Basic formulations are provided for three adaptive-stenciling methods: essentially non-oscillatory (ENO), weighted essentially non-oscillatory (WENO), and energy-stable weighted essentially non-oscillatory (ESWENO) schemes. Examples are presented to display some of the relevant properties of these schemes in solving one-dimensional and two-dimensional linear and nonlinear hyperbolic differential equations with discontinuities.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Otis, Collin
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairGivi, Peymanpeg10@pitt.eduPEG10
Committee MemberTo, Albert Calbertto@pitt.eduALBERTTO
Committee MemberTrenchea, Catalin Strenchea@pitt.eduTRENCHEA
Date: 30 September 2010
Date Type: Completion
Defense Date: 19 July 2010
Approval Date: 30 September 2010
Submission Date: 22 July 2010
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: MSME - Master of Science in Mechanical Engineering
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: cfd; computational fluid dynamics; discontinuous; fluid mechanics; flux; high order; hypersonic; numerical methods; numerical scheme; numerics; subsonic; supersonic; flow; shock
Other ID:, etd-07222010-105339
Date Deposited: 10 Nov 2011 19:52
Last Modified: 15 Nov 2016 13:46


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