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High-order Finite Volume Methods for...

Felker, Kyle Gerard.

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High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics./
Author:	Felker, Kyle Gerard.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	249 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Contained By:	Dissertations Abstracts International81-05B.
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22621965
ISBN:	9781687984470

High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics.
Felker, Kyle Gerard.

High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 249 p.

Source: Dissertations Abstracts International, Volume: 81-05, Section: B.

Thesis (Ph.D.)--Princeton University, 2019.

This item must not be sold to any third party vendors.

Finite volume (FV) methods with high-order accuracy have attracted the interest of computational astrophysicists who are interested in modeling the most challenging physical regimes. With their large numerical diffusivity, popular second-order accurate FV codes are incapable of resolving many such problems using current high-performance computing (HPC) hardware. High-order FV methods may perform more efficiently than their lower-order counterparts while continuing to offer the robust shock-capturing properties that are essential for simulating the highly compressible flows that often occur in astrophysical phenomena.We present a novel fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution to semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena++ astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth- order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.The fourth-order FV method is implemented within the open-source Athena++ framework. A comprehensive set of validation and performance tests are added and directly integrated in the collaborative development environment using continuous integration services. Other automated tools and practices are established to ensure the manageability of the codebase as it matures.We apply the solver to a set of computationally demanding 2D benchmarks based on the Kelvin- Helmholtz instability. The fourth-order and several related high- order FV methods produce significantly more accurate solutions than the second-order method. By comparing the computational performance of these schemes on modern multi-core, distributed-memory architectures, we show that the high-order solvers are capable of much greater efficiency (time- to-solution for a given level of accuracy) than the second-order alternatives.

ISBN: 9781687984470Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Finite volume method

High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics.
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245 1 0 $a High-order Finite Volume Methods for Magnetohydrodynamics with Applications in Computational Astrophysics.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 249 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
500 $a Advisor: Stone, James M.
502 $a Thesis (Ph.D.)--Princeton University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Finite volume (FV) methods with high-order accuracy have attracted the interest of computational astrophysicists who are interested in modeling the most challenging physical regimes. With their large numerical diffusivity, popular second-order accurate FV codes are incapable of resolving many such problems using current high-performance computing (HPC) hardware. High-order FV methods may perform more efficiently than their lower-order counterparts while continuing to offer the robust shock-capturing properties that are essential for simulating the highly compressible flows that often occur in astrophysical phenomena.We present a novel fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution to semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena++ astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth- order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.The fourth-order FV method is implemented within the open-source Athena++ framework. A comprehensive set of validation and performance tests are added and directly integrated in the collaborative development environment using continuous integration services. Other automated tools and practices are established to ensure the manageability of the codebase as it matures.We apply the solver to a set of computationally demanding 2D benchmarks based on the Kelvin- Helmholtz instability. The fourth-order and several related high- order FV methods produce significantly more accurate solutions than the second-order method. By comparing the computational performance of these schemes on modern multi-core, distributed-memory architectures, we show that the high-order solvers are capable of much greater efficiency (time- to-solution for a given level of accuracy) than the second-order alternatives.
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650 4 $a Applied mathematics. $3 2122814
650 4 $a Computational physics. $3 3343998
650 4 $a Astrophysics. $3 535904
653 $a Finite volume method
653 $a Godunov method
653 $a Kelvin-Helmholtz instability
653 $a Magnetohydrodynamics
653 $a Numerical methods
653 $a Software engineering
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690 $a 0216
690 $a 0596
710 2 $a Princeton University. $b Applied and Computational Mathematics. $3 3182352
773 0 $t Dissertations Abstracts International $g 81-05B.
790 $a 0181
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22621965