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Analysis of Time Filters in Multistep Methods

Hurl, Nicholas (2017) Analysis of Time Filters in Multistep Methods. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Geophysical flow simulations have evolved sophisticated implicit-explicit time stepping methods (based on fast-slow wave splittings) followed by time filters to control any unstable models that result. Time filters are modular and parallel. Their effect on stability of the overall process has been tested in numerous simulations, but never analyzed. Stability is proven herein for the Crank-Nicolson Leapfrog (CNLF) method with the Robert-Asselin (RA) time filter and for the Crank-Nicolson Leapfrog method with the Robert-Asselin-Williams (RAW) time filter for systems by energy methods. We derive an equivalent multistep method for CNLF+RA and CNLF+RAW and stability regions are obtained. The time step restriction for energy stability of CNLF+RA is smaller than CNLF and CNLF+RAW time step restriction is even smaller. Numerical tests find that RA and RAW add numerical dissipation.

This thesis also shows that all modes of the Crank-Nicolson Leap Frog (CNLF) method are asymptotically stable under the standard timestep condition.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Hurl, Nicholasndh12@pitt.edundh12
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairLayton,
Committee MemberTrenchea,
Committee MemberJiang,
Committee MemberSomlinski,
Date: 25 June 2017
Date Type: Publication
Defense Date: 9 September 2016
Approval Date: 25 June 2017
Submission Date: 25 January 2017
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 64
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Conditional Stability, IMEX methods, Crank-Nicolson, Leapfrog, Robert--Asselin--Williams filter
Date Deposited: 25 Jun 2017 22:12
Last Modified: 25 Jun 2017 22:12


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