# Vorlesungsbeispiele Erhaltungsgleichungen

## Linear Transport Equation 1D

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

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

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

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

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

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

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

## Shocktube

### Density

Vijayasundaram-Scheme

van-Leer Scheme

### Pressure

Vijayasundaram-Scheme

van-Leer Scheme