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Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables

Yao, Zhen (2024) Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Magnetohydrodynamics (MHD) describes the interaction between the electrically conducting fluids and the electromagnetic fields. The report is devoted to the design and analysis of a partitioned, iterative, midpoint (PIM) algorithm of second-order convergence in time for the evolutionary MHD system in Elsässer variables. To reduce the computational costs of the non-linear solver, we partitioned the full system at each iteration and thus solve two subproblems in parallel. We prove that partitioned iterations converge to the numerical solutions of the coupled monolithic problem under certain mild time restriction. The stability of the PIM method and its error analysis show that the algorithm with arbitrary time grids is unconditionally conservative in energy, cross-helicity and magnetic helicity and numerical solutions are of second-order convergence.

Moreover, the time adaptive mechanism based on local truncation error criterion is implement into the constant time-step PIM method, which helps the variable step algorithm balance accuracy and time efficiency. Several numerical tests support the theoretical findings and verify the advantages of time adaptivity.

Moreover, we construct a partitioned, iterative DLN (Dahlquist, Liniger and Nevanlinna) algorithm for this MHD system in Elsässer variables, which also partitions the full nonlinear system at each iteration. We also analyze the conservation of the energy, cross-helicity and magnetic-helicity, followed by the variable step stability and error analysis.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Yao, Zhenzhy76@pitt.edu43708850009-0000-9248-5903
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairTrenchea, Catalintrenchea@pitt.edu
Committee MemberNeilan, Michaelneilan@pitt.edu
Committee MemberLayton, williamwjl@pitt.edu
Committee MemberLabovsky, Alexanderaelabovs@mtu.edu
Date: 20 December 2024
Date Type: Publication
Defense Date: 3 December 2024
Approval Date: 20 December 2024
Submission Date: 4 December 2024
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 88
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: Magnetohydrodynamics, Elsässer variables, partitioned algorithms, iterative methods, DLN methods, second-order accurate, variable steps, time adaptivity
Date Deposited: 20 Dec 2024 14:49
Last Modified: 20 Dec 2024 14:49
URI: http://d-scholarship.pitt.edu/id/eprint/47172

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