High Order H(div) Discontinuous Galerkin Methods for MHD Equations

1 online resource (112 pages) : PDF

2016

University of North Carolina at Charlotte

In this dissertation, we investigate the divergence-free discontinuous Galerkin method using the $\mathcal{H}$(\textbf{div}) basis, to solve the nonlinear ideal magnetohydrodynamics (MHD) equations. This is a novel approach to ensure the divergence-free condition on the magnetic field. The idea is to add on each element extra bubble functions from the same order hierarchical $\mathcal{H}$(\textbf{div})-conforming basis to reduce the higher order divergence, and then extra constant edge functions to remove the constant term of divergence. As a consequence, this method has a smaller computational cost than the traditional discontinuous Galerkin method with standard piecewise polynomial spaces. We formulate the discontinuous Galerkin method using the $\mathcal{H}$(\textbf{div})-conforming basis and perform extensive two-dimensional numerical experiments for both smooth solutions and solutions with discontinuities. The computational results show that the global divergence is largely reduced, but with a relatively small increase in the error of the numerical solution itself.

doctoral dissertations

Mathematics

Ph.D.

Discontinuous Galerkin Method
Divergence-Free Solutions
H(div) Basis Function
Magnetohydrodynamics (mhd) Equations

Mathematics

Cai, Wei
Deng, Shaozhong

Cai, Wei
Deng, Shaozhong
Chen, Duan
Su, Zhengchang

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2016.

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Wu_uncc_0694D_11223

http://hdl.handle.net/20.500.13093/etd:1591