Related papers: Divergence-Free Adaptive Mesh Refinement for Magne…
Balsara (2001) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD was shown in Balsara…
In this paper we study the problem of divergence-free numerical MHD and show that the work done so far still has four key unresolved issues. We resolve those issues in this paper. The problem of reconstructing MHD flow variables with…
Balsara (2001, J. Comput. Phys., 174, 614) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes…
There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
We present a new method for evolving the equations of magnetohydrodynamics (both Newtonian and relativistic) that is capable of maintaining a divergence-free magnetic field ($\nabla \cdot \mathbf{B} = 0$) on adaptively refined, conformally…
We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called…
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an…
Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…
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…
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…
We have written and tested a new general relativistic magnetohydrodynamics (GRMHD) code, capable of evolving MHD fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system…
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is based on the full…
In the present paper, we present an adaptive mesh refinement(AMR) approach designed for the discontinuous Galerkin method for conservation laws. The block-based AMR is adopted to ensure the local data structure simplicity and the…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO…
GAMER, a parallel Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement hydrodynamic code, has been extended to support magnetohydrodynamics (MHD) with both the corner-transport-upwind (CTU) and MUSCL-Hancock schemes and the…