iluckyyang/numerical_exercises

An introduction to numerical methods for astrophysical hydrodynamics

Computational Hydrodynamics for Astrophysics

part of the Open Astrophysics Bookshelf

Notes on numerical methods for computational astrophysical hydrodynamics.

These notes describe the way I think about the numerical methods commonly used with grid-based codes in astrophysical hydrodynamics. The notes are written in LaTeX, and should build by typing 'make' in the main directory.

Working implementations for all of the solvers are contained either in the main pyro code or in the set of hydro examples, both referenced below.

Chapters

The following chapters are mostly written:

• Simulation Overview
• Finite-Volume Grids
• Advection
• Burgers' Equation
• Euler Equations
• Elliptic Equations and Multigrid
• Diffusion
• Multiphysics Applications
• Incompressible Flow and Projection Methods
• Low Mach Number Methods

The following are things I'd like to add in the next 1-2 years:

• Standard Hydro Test Problems
• Fluid Instabilities
• Rotation and Self-gravity
• Radiation Hydrodynamics
• MHD
• AMR
• Mapped Grids

The following are things hopefully will eventually get written:

• Relativisitc Flows
• Higher-Order Methods
• Implicit Hydrodynamics

Getting PDFs and Source

A PDF version of these notes is available at:

http://bender.astro.sunysb.edu/hydro_by_example/CompHydroTutorial.pdf

There are two sets of companion codes that go along with these notes:

• hydro_examples: https://github.com/zingale/hydro_examples

  simple, standalone, 1-d solvers that illustrate the basic ideas.

• pyro: https://github.com/zingale/pyro2

  pyro is a 2-d full simulation code designed with simplicity in mind that implements the core solvers described in these notes along with various test problems.