Related papers: Second Order Accurate Schemes for Magnetohydrodyna…
We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented…
This paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The…
In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is…
The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric…
We propose a second-order accurate semi-implicit and well-balanced finite volume scheme for the equations of ideal magnetohydrodynamics (MHD) including gravitational source terms. The scheme treats all terms associated with the acoustic…
A second order accurate, linear numerical method is analyzed for the Landau-Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the…
Due to the prevalence of magnetic fields in astrophysical environments, magnetohydrodynamic (MHD) simulation has become a basic tool for studying astrophysical fluid dynamics. To further advance the precision of MHD simulations, we have…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We…
We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation…
We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in…
We present a high order one-step ADER-WENO finite volume scheme with space-time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous…
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum,…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid…
Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
This work combines the consistency in lower-order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured non-uniform meshes. This…
The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use…