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Isogeometric analysis of the steady-state incompressible mhd equations

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Title: Isogeometric analysis of the steady-state incompressible mhd equations
Authors: Ahn, J
Bluck, M
Item Type: Journal Article
Abstract: This paper presents an isogeometric (IGA) solver for steady-state incompressiblemagnetohydrodynamics (MHD). MHD is the study of the behavior of electrically conducting fluidsand can be viewed mathematically as a coupled system: the Navier--Stokes equations (for the fluid)and a reduced form of Maxwell's equations (for the electromagnetic field). A key feature of MHDflow is the potential development of very strong shear, usually in proximity to walls. This resultsin two correlated demands on numerical simulation: the need to represent the geometry and thenear-wall shear accurately. In addition, for both the Navier--Stokes and the Maxwell's equations,appropriate discretizations are required for the problem to be well-posed. IGA analysis is a variant ofthe conventional finite element (FE) method, but utilizing the underlying approximations commonlyused in computer-aided design (CAD) to represent geometry, basis functions, and test functions.As a result, IGA can represent curved shapes such as circles and conic sections exactly using B-splines and nonuniform rational B-splines (NURBS). Furthermore, IGA can obtain much improvedaccuracy in the computed solution, for a given number of degrees of freedom, due to its inherentsmoothness and higher continuity of basis functions when compared with standard FE and finitevolume (FV) methods. To address the issue of well-posedness, a set of stable IGA discretizationsfor the Navier--Stokes and Maxwell's equations is developed and incorporated into the IGA solver.A detailed convergence study is carried out to verify the convergence, accuracy, and performance ofthe IGA scheme for certain benchmark cases.
Issue Date: 11-Apr-2019
Date of Acceptance: 28-Jan-2019
URI: http://hdl.handle.net/10044/1/67925
DOI: https://doi.org/10.1137/18M1182401
ISSN: 1064-8275
Publisher: Society for Industrial and Applied Mathematics
Start Page: B396
End Page: B424
Journal / Book Title: SIAM Journal on Scientific Computing
Volume: 41
Issue: 2
Copyright Statement: © 2019, Society for Industrial and Applied Mathematics
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Numerical & Computational Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0802 Computation Theory and Mathematics
Publication Status: Published
Online Publication Date: 2019-04-11
Appears in Collections:Faculty of Engineering
Mechanical Engineering