On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method.
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Publication:1428651
DOI10.1016/j.jcp.2003.09.016zbMath1087.76074arXivastro-ph/0310183OpenAlexW2088337589MaRDI QIDQ1428651
Publication date: 29 March 2004
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/astro-ph/0310183
Finite volume methods applied to problems in fluid mechanics (76M12) Magnetohydrodynamics and electrohydrodynamics (76W05)
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Cites Work
- Non-oscillatory central differencing for hyperbolic conservation laws
- Divergence- and curl-preserving prolongation and restriction formulas
- Local adaptive mesh refinement for shock hydrodynamics
- Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
- The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
- On Godunov-type schemes for magnetohydrodynamics. I: A model system
- Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids
- A simple finite difference scheme for multidimensional magnetohydrodynamical equations
- A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
- Roe matrices for ideal MHD and systematic construction of Roe matrices for systems of conservation laws
- The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
- Hyperbolic divergence cleaning for the MHD equations
- A solution-adaptive upwind scheme for ideal magnetohydrodynamics
- Conservative and orthogonal discretization for the Lorentz force.
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
- On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
- Convex Entropies and Hyperbolicity for General Euler Equations
- Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
- An efficient shock-capturing central-type scheme for multidimensional relativistic flows
- Notes on the Eigensystem of Magnetohydrodynamics
- Systems of conservation laws
- Divergence-free adaptive mesh refinement for magnetohydrodynamics.