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Locally-Implicit Lax-Wendroff Discon...

Pelakh, Ian,

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Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations // Ian Pelakh.
Author:	Pelakh, Ian,
Description:	1 electronic resource (80 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Computational physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31938211
ISBN:	9798286431014

Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations /
Pelakh, Ian,

Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations /Ian Pelakh. - 1 electronic resource (80 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

The ideal magnetohydrodynamic (MHD) equations are a system of equations describing the behavior of electrically conducting fluids. The MHD system can be written in symmetric hyperbolic form, but only if an additional condition is satisfied: the magnetic field must be divergence-free, ∇ · B =0. There have been many proposed methods for how to modify the system or methods to account for this additional constraint, such as hyperbolic divergence cleaning and constrained transport. This work develops a novel Lax-Wendroff discontinuous Galerkin finite element method to solve the ideal magnetohydrodynamic equations. New limiters are designed to control unphysical oscillations and guarantee density and pressure positivity. Each time step of the resulting numerical method is equipped with a constrained transport step that enforces the divergence-free property on the discrete magnetic field. The resulting method is tested on a series of standard cases for both the compressible Euler and the ideal magnetohydrodynamic equations, demonstrating the order of accuracy of the scheme on smooth problems, as well as the ability of the scheme to prevent unphysical oscillations and positivity violations on examples with shock waves.

English

ISBN: 9798286431014Subjects--Topical Terms:

3343998
Computational physics.
Subjects--Index Terms:

Numerical methods

Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations /
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245 1 0 $a Locally-Implicit Lax-Wendroff Discontinuous Galerkin Schemes with Constrained Transport for the Ideal Magnetohydrodynamic Equations / $c Ian Pelakh.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (80 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Rossmanith, James Committee members: Parshad, Rana; Wu, Zhijun; Songting, Luo; Yan, Jue.
502 $b Ph.D. $c Iowa State University $d 2025.
520 $a The ideal magnetohydrodynamic (MHD) equations are a system of equations describing the behavior of electrically conducting fluids. The MHD system can be written in symmetric hyperbolic form, but only if an additional condition is satisfied: the magnetic field must be divergence-free, ∇ · B =0. There have been many proposed methods for how to modify the system or methods to account for this additional constraint, such as hyperbolic divergence cleaning and constrained transport. This work develops a novel Lax-Wendroff discontinuous Galerkin finite element method to solve the ideal magnetohydrodynamic equations. New limiters are designed to control unphysical oscillations and guarantee density and pressure positivity. Each time step of the resulting numerical method is equipped with a constrained transport step that enforces the divergence-free property on the discrete magnetic field. The resulting method is tested on a series of standard cases for both the compressible Euler and the ideal magnetohydrodynamic equations, demonstrating the order of accuracy of the scheme on smooth problems, as well as the ability of the scheme to prevent unphysical oscillations and positivity violations on examples with shock waves.
546 $a English
590 $a School code: 0097
650 4 $a Computational physics. $3 3343998
650 4 $a Applied mathematics. $3 2122814
650 4 $a Theoretical physics. $3 2144760
650 4 $a Fluid mechanics. $3 528155
653 $a Numerical methods
653 $a Magnetohydrodynamic equations
653 $a Divergence-free magnetic field
653 $a Discontinuous Galerkin method
653 $a Shock waves
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690 $a 0753
690 $a 0204
690 $a 0364
710 2 $a Iowa State University. $b Mathematics. $e degree granting institution. $3 3822982
720 1 $a Rossmanith, James $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0097
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31938211