Homepage for the course
"Introduction to the numerical methods of fluid dynamics"
MSc in applied mathematics, autumn semester, 2024
Lectures and practices
Materials to download for this course
•
Lecture notes in Hungarian to the second half of the semester
available here (the material for this semester: Section 2)
•
Problems, exercises to the practices available here.
Note that both of them will be updated from week to week: Please download always the current version.
•
Sample Matlab codes with the Lax--Friedrichs scheme,
the Lax--Wendroff scheme and the
Godunov scheme are available here. For the reconstruction schemes, you have to use the
minmod function, the
Godunov flux function and the code for the
reconstruction scheme.
For the Euler equations, you have to use the
real flux function, the
Lax - Friedrichs (numerical) flux function and the code for the
main code programs.
Further literature
• R. LeVeque: Numerical Methods for Conservation Laws, Birkhauser, 1992. - Very good widely used textbook. Also other versions and editions exist.
• E. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1997. - Very good widely used textbook.
• L. Evans: Partial DIfferential Equations, Springer, 2nd ed. 2010 - Best book on PDE's: no numerics, just to understand equations, schocks.
•
Or simply Google: "numerical methods for conservation laws"
you will find a number of nice lecture notes.