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.
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
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.