The Athena++ Adaptive Mesh Refinement Framework: Multigrid Solvers for Self-Gravity

Abstract

We describe the implementation of multigrid solvers in the Athena++ adaptive mesh refinement (AMR) framework and their application to the solution of the Poisson equation for self-gravity. The new solvers are built on top of the AMR hierarchy and TaskList framework of Athena++ for efficient parallelization. We adopt a conservative formulation for the Laplacian operator that avoids artificial accelerations at level boundaries. Periodic, fixed, and zero-gradient boundary conditions are implemented, as well as open boundary conditions based on a multipole expansion. Hybrid parallelization using both MPI and OpenMP is adopted, and we present results of tests demonstrating the accuracy and scaling of the methods. On a uniform grid we show multigrid significantly outperforms methods based on FFTs, and requires only a small fraction of the compute time required by the (highly optimized) magnetohydrodynamic solver in Athena++. As a demonstration of the capabilities of the methods, we present the results of a test calculation of magnetized protostellar collapse on an adaptive mesh.

arXiv comment28 pages, 13 figures, submitted to AAS Journals

References in corpus (29)

• Enzo: An Adaptive Mesh Refinement Code for Astrophysics
• Adaptive Refinement Tree - a new high-resolution N-body code for cosmological simulations
• The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers
• A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
• Magnetic processes in a collapsing dense core. I Accretion and Ejection
• Magnetohydrodynamics on an unstructured moving grid
• An Extension of the Athena++ Code Framework for GRMHD Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
• A Module for Radiation Hydrodynamic Calculations With ZEUS-2D Using Flux-Limited Diffusion
• Radiation Magnetohydrodynamic Simulations of Protostellar Collapse: Non-Ideal Magnetohydrodynamic Effects and Early Formation of Circumstellar Disks
• A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
• A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes
• A Godunov Method for Multidimensional Radiation Magnetohydrodynamics based on a variable Eddington tensor
• Grand Design Spiral Arms in A Young Forming Circumstellar Disk
• First MHD Simulation of Collapse and Fragmentation of Magnetized Molecular Cloud Cores
• Interchange instability in an accretion disc with a poloidal magnetic field
• Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths
• The Matryoshka Run: Eulerian Refinement Strategy to Study Statistics of Turbulence in Virialized Cosmic Structures
• Self-gravitational Magnetohydrodynamics with Adaptive Mesh Refinement for Protostellar Collapse
• An Implicit Finite Volume Scheme to Solve the Time Dependent Radiation Transport Equation Based on Discrete Ordinates
• GRAthena++: puncture evolutions on vertex-centered oct-tree AMR
• Disk Formation in Magnetized Dense Cores with Turbulence and Ambipolar Diffusion
• A New Way to Conserve Total Energy for Eulerian Hydrodynamic Simulations with Self-Gravity
• A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC
• A Fast Poisson Solver of Second-Order Accuracy for Isolated Systems in Three-Dimensional Cartesian and Cylindrical Coordinates
• An Extension of the Athena++ Framework for General Equations of State
• An Extension of the Athena++ Framework for Fully Conservative Self-Gravitating Hydrodynamics
• Unravelling cosmic velocity flows: a Helmholtz-Hodge decomposition algorithm for cosmological simulations
• Self-gravitational Force Calculation of Second Order Accuracy Using Multigrid Method on Nested Grids
• A simple and efficient solver for self-gravity in the DISPATCH astrophysical simulation framework

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• Prestellar Cores in Turbulent Clouds: Numerical Modeling and Evolution to Collapse
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• Instability and Evolution of Shocked Clouds Formed by Orthogonal Collisions between Magnetized Filamentary Molecular Clouds
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