The content introduces a novel approach to discretize ideal MHD equations using variational principles and finite element methods. By leveraging differential forms and Lie derivatives, the scheme conserves key properties like mass, entropy, and energy. The methodology ensures stability and accuracy in simulations by preserving essential invariants such as total mass and solenoidal characteristics of the magnetic field. The proposed time discretization maintains conservation laws and reversibility. Specific choices for discrete spaces, operators, and projections are detailed to enhance numerical results.
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by Valentin Car... في arxiv.org 02-29-2024
https://arxiv.org/pdf/2402.02905.pdfاستفسارات أعمق