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Coding Solvers for Fluids

Overview

Using These Notes
Why Write Your Own Hydro Code?

Advection

Linear Advection
Finite-Volume Discretization
A Grid Class and Ghost Cells
First-Order Accurate Time Update
Basic Driver
Advection Test Problem
Implementing First Order Advection
Measuring Convergence
Second-order Advection

Advection Exercises

Different Limiters
Characteristic Tracing
Two-dimensional Advection
Piecewise Parabolic Reconstruction for Advection
Burgers’ Equation
- Burgers’ Riemann Problem
- Solving Burger’s equation

Compressible Euler Equations

Euler Equations
Euler Equations Eigensystem
Euler Riemann Problem
Sampling the Riemann Solution
Second-Order Euler Solver

Euler Solver Exercises

Measuring Convergence of our Euler Solver
Time Integration
HLL Riemann Solver
Non-conservation?
Sedov Explosion and Spherical Symmetry

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By Michael Zingale

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