Vorlesungsbeispiele Erhaltungsgleichungen

Scalar Conservation Laws

 

Linear Transport Equation 1D

The example left- and rightsided differences is the solution of the problem

erhaltungs_linear.gif

calculated with left and rightsided differences.

top : leftsided differences
bottom: rightsided differences.

 

The example comparison Lax-Friedrichs, Lax-Wendroff, min-mod Limiter is the solution of the problem

 erhaltungs_linear.gif

 

calculated with Lax-Friedrich, Lax-Wendof and min-mod limiter scheme.

 

top : Lax-Friedrichs-scheme
middle: Lax-Wendroff-scheme
bottom: min-mod limiter scheme.

 

The example comparison Lax-Friedrichs, discontinuous galerkin, min-mod limiter is the solution of the problem

 

 erhaltungs_linear.gif

calculated with Lax-Freidrichs, discontinuous galerkion and min-mod limiter scheme.

top : Lax-Friedrichs-scheme
middle: discontinuous Galerkin scheme
bottom: min-mod limiter scheme.

 

The example comparison Lax-Wendroff, Warming & Beam, min-mod limiter is the solution of the problem

 

 erhaltungs_linear.gif

calculated with Lax-Wendroff, Warming & Beam and min-mod limiter scheme.

top : Lax-Wendroff-scheme
middle: Warming & Beam scheme
bottom: min-mod limiter scheme.

 

Burgers Equation 1D

The example comparison Lax-Friedrichs, Engquist-Osher, Godunov is the solution of the problem

erhaltungs_burgers.gif

 

calculated with Lax-Friedrichs, Engquist-Osher and Godunov-scheme.

top : Lax-Friedrichs-scheme
middle: Engquist-Osher-scheme
bottom: Godunov-scheme.

 

Shocktube

Density

adaptive scheme:

 

comparison adaptive - not adaptive scheme

 

Vijayasundaram-Scheme

 

van-Leer Scheme

 

Pressure

Vijayasundaram-Scheme

 

van-Leer Scheme

 

Two cylinders in a supersonic flow

Density

Grid and adaptation efficiency

 

Traceroutes

 

Particle tracing