Doctoral Dissertations

Keywords and Phrases

ensemble algorithm; MHD; SAV; Uncertainty Quantification; unconditional stability

Abstract

"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate the efficiency and long-time accuracy of the proposed algorithms"--Abstract, p. iv

Advisor(s)

Han, Daozhi
Jiang, Nan

Committee Member(s)

He, Xiaoming
Zhang, Yanzhi
Singler, John R.
Guirong, Yan

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Computational and Applied Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2023

Pagination

xiii, 80 pages

Note about bibliography

Includes_bibliographical_references_(pages 75-79)

Rights

© 2023 John Austin Carter, All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12291

Electronic OCLC #

1426051408

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