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Isogeometric analysis of the steady-state incompressible mhd equations
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![]() | Accepted version | 5.2 MB | Adobe PDF | View/Open |
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 Mathematics isogeometric incompressible steady-state MHD FINITE-ELEMENT APPROXIMATION CONFORMING B-SPLINES MAGNETOHYDRODYNAMICS SINGULARITIES SYSTEMS SCHEME FORMS FLOW 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: | Mechanical Engineering Faculty of Engineering |