Contents

• Motivation
• The advection equation
  • Background
  • Order of Convergence of the Method
  • Implementation of a naive piecewise linear reconstruction
  • Velocity $v(x)=x$
  
  
• Burgers Equation
  • Background
  • Implementation of the Roe and Riemann Exact Solver
  • Exact and Approximated evolution of the Gaussian Profile
  • Models A,B, and C: Pulse Profile Evolution
  • Triangular Profile
  
  
• 1-d Relativistic Fluid in Flat Space-time
  • The Riemann problem in special relativistic hydrodynamics
  • Primitive Reconstruction, Primitive Averaging
  • Conservative Reconstruction, Primitive Averaging
  • Primitive Reconstruction, Conservative Averaging
  • Conservative Reconstruction, Conservative Averaging
  
  
• Appendix: Basics of Godunov Methods
  • Roe Solver
  
  
• Bibliography