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- W2962974889 abstract "This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas." @default.
- W2962974889 created "2019-07-30" @default.
- W2962974889 creator A5000404410 @default.
- W2962974889 creator A5045031334 @default.
- W2962974889 creator A5061459085 @default.
- W2962974889 creator A5072910798 @default.
- W2962974889 date "2018-03-13" @default.
- W2962974889 modified "2023-10-12" @default.
- W2962974889 title "Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics" @default.
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