A -order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions
arXiv:2310.11831 · doi:10.1016/j.jcp.2023.112701
Abstract
We present a novel implementation of a genuinely -order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism. The scheme introduces several novel aspects when compared to its predecessors yielding a more efficient computational tool. Among the most relevant ones, our scheme exploits pointwise to pointwise reconstructions (rather than one-dimensional finite volume ones), employs the generic upwind constrained transport averaging and sophisticated limiting strategies that include both a discontinuity detector and an order reduction procedure. Selected numerical benchmarks demonstrate the accuracy and robustness of the method.
arXiv comment30 pages, 14 figures
References in corpus (32)
- PLUTO: a Numerical Code for Computational Astrophysics
- HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics
- An Unsplit Godunov Method for Ideal MHD via Constrained Transport
- The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
- A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
- An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
- ECHO: an Eulerian Conservative High Order scheme for general relativistic magnetohydrodynamics and magnetodynamics
- Second Order Accurate Schemes for Magnetohydrodynamics With Divergence-Free Reconstruction
- On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method
- A Divergence-Free Upwind Code for Multidimensional Magnetohydrodynamic Flows
- Very High Order $\PNM$ Schemes on Unstructured Meshes for the Resistive Relativistic MHD Equations
- High Order Upwind Schemes for Multidimensional Magnetohydrodynamics
- Divergence-Free Reconstruction of Magnetic Fields and WENO Schemes for Magnetohydrodynamics
- An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics
- High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
- A five-wave HLL Riemann solver for relativistic MHD
- Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for Multi-Dimensional Flow
- A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics
- A conservative orbital advection scheme for simulations of magnetized shear flows with the PLUTO code
- An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
- A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
- Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics
- A Simple and Accurate Riemann Solver for Isothermal MHD
- Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
- Magnetohydrodynamic Simulation Code CANS+: Assessments and Applications
- Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM
- Systematic construction of upwind constrained transport schemes for MHD
- Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term
- A high-order weighted finite difference scheme with a multi-state approximate Riemann solver for divergence-free magnetohydrodynamic simulations
- A variable high-order shock-capturing finite difference method with GP-WENO
- The Piecewise Cubic Method (PCM) for Computational Fluid Dynamics
- A comparison of approximate non-linear Riemann solvers for Relativistic MHD
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- PyPLUTO: a data analysis Python package for the PLUTO code
- High-order finite-volume integration schemes for subsonic magnetohydrodynamics
- The Yin-Yang Magnetic Flux Eruption (Yin-Yang-MFE) Code: A Global Corona Magnetohydrodynamic Code with the Yin-Yang grid