Cosmological Adaptive Mesh Refinement

We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive particle--mesh methods for collisionless particles. The basis for our method is the structured adaptive mesh refinement (AMR) algorithm of Berger & Collela (1989), which we have extended to cosmological hydro + N-body simulations. The resulting multiscale hybrid method is a powerful alternative to particle-based methods in current use. The choices we have made in constructing this algorithm are discussed, and its performance on the Zeldovich pancake test problem is given. We present a sample application of our method to the problem of first structure formation. We have achieved a spatial dynamic range $L_{box}/\Delta x > 250,000$ in a 3D multispecies gas + dark matter calculation, which is sufficient to resolve the formation of primordial protostellar cloud cores starting from linear matter fluctuations in an expanding FRW universe.Comment: 14 pages, 3 figures (incl. one large color PS) to appear in "Numerical Astrophysics 1998", eds. S. Miyama & K. Tomisaka, Tokyo, March 10-13, 199

Adaptive Mesh Refinement for Singular Current Sheets in Incompressible Magnetohydrodynamic Flows

The formation of current sheets in ideal incompressible magnetohydrodynamic flows in two dimensions is studied numerically using the technique of adaptive mesh refinement. The growth of current density is in agreement with simple scaling assumptions. As expected, adaptive mesh refinement shows to be very efficient for studying singular structures compared to non-adaptive treatments.Comment: 8 pages RevTeX, 13 Postscript figure

Wrinkling prediction with adaptive mesh refinement

An adaptive mesh refinement procedure for wrinkling prediction analyses is presented. First the\ud critical values are determined using Hutchinson’s bifurcation functional. A wrinkling risk factor is then\ud defined and used to determined areas of potential wrinkling risk. Finally, a mesh refinement is operate

Relativistic MHD with Adaptive Mesh Refinement

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 method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Adaptive Mesh Refinement for Characteristic Codes

The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon system of equations in spherical symmetry. We discuss how the algorithm can trivially be generalized to higher dimensional systems, and suggest a method that can be used to parallelize a characteristic code.Comment: 36 pages, 17 figures; updated to coincide with journal versio

Adaptive Mesh Refinement for Characteristic Grids

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in 2-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null \emph{slices}. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both 2nd and 4th order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3 document class, includes C++ source code. Changes from v1: revised in response to referee comments: many references added, new figure added to better explain the algorithm, other small changes, C++ code updated to latest versio