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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
Repository
Open issue
Index
