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: Theory
Euler Equations: Numerical Methods
Elliptic Equations and Multigrid
Diffusion
Model Multiphysics Problems
Reactive Flow
Planning a Simulation
Incompressible Flow and Projection Methods
Low Mach Number Methods

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

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://open-astrophysics-bookshelf.github.io/numerical_exercises/

(this PDF is automatically generated by a Github action each time changes are pushed to main.)

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/python-hydro/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.

License

albertobottopoala/numerical_exercises

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