Numerical methods for fluid dynamics

Credits: 2

Carga Horária Total: 30 h


The goal of this reading course (curso de leitura) is to give us the theoretical rudiments for numerically solving the conservation equations of fluid dynamics—and by extension magnetohydrodynamics (MHD). In particular, we aim at having a solid understanding of the Godunov method.


The equations of fluid dynamics. Hyperbolic PDEs. Properties of Euler equations. Riemann problem. Overview of numerical methods. Godunov method.


Method: Course attendants will meet on a weekly basis to discuss the topic assigned for the corresponding week. All attendants are expected to study the course material before each meeting.

Criteria: Discussions to make sure everybody is on the same page and have a solid grasp of physical concepts and numerical techniques. Numerical exercises with C or Python.


  • Bodenheimer, P. et al. Numerical methods for astrophysics: An introduction. 2007, Taylor & Francis
  • Gourgoulhon, E. 3+1 Formalism in General Relativity: Bases of Numerical Relativity. 2012, Springer
  • Landau, L. D., Lifshitz, E. M. Fluid mechanics. 1987, Butterworth-Heinemann
  • Laney, C. B. Computational Gasdynamics. 1998, Cambridge Univ. Press
  • LeVeque, R. J. Finite Volume Methods for Hyperbolic Problems. 2002, Cambridge Univ. Press
  • Rezzolla, L., Zanotti, O. Relativistic hydrodynamics. 2013, Oxford
  • Toro, E. F. Riemann Solvers and Numerical Methods for Fluid Dynamics. 2009, Springer 


University of São Paulo / Associate Professor

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