Yao, Zhen
(2024)
Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
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
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| 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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