Related papers: Adaptive Mesh Refinement and Relativistic MHD
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave).…
This article develops a general-purpose adaptive sampler that approximates the target density by a mixture of multivariate t densities. The adaptive sampler is based on reversible proposal distributions each of which has the mixture of…
We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the…
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides several high resolution, shock capturing schemes which are constructed to maintain…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and…
This paper develops high-order accurate entropy stable (ES) adaptive moving mesh finite difference schemes for the two- and three-dimensional special relativistic hydrodynamic (RHD) and magnetohydrodynamic (RMHD) equations, which is the…
Recently, compressible magnetohydrodynamics (MHD) has been elegantly formulated in terms of Lie derivatives. This paper exploits the geometrical properties of the Lie bracket to give new insights into the properties of compressible MHD…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $\Lambda$-convex hull, the latter providing inequalities…
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in Gamma-Ray Burst sources. The SRHD equations are…
We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, this is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of…
The paper presents a comparative analysis of different commercial and academic software. The comparison aims to examine how the integrated adaptive grid refinement methodologies can deal with challenging, electromagnetic-field related…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are…
We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a symmetric system for the vector of primitive…
We present a novel spectral solver for general relativistic magnetohydrodynamics on dynamical spacetimes. By combining a high order discontinuous spectral method on mapped Chebyshev Fourier grids, our scheme attains exponential convergence.…
In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have…
Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the…