Scalar Conservation Laws

Linear Transport Equation 1D
left- and rightsided differences
Lax-Friedrichs, Lax-Wendroff, min-mod Limiter
Lax-Friedrichs, Discontinuous Galerkin, min-mod Limiter
Lax-Wendroff, Warming & Beam, min-mod Limiter
Burgers Equation 1D
Lax-Friedrichs, Engquist-Osher, Godunov
Systems of conservation laws

shocktube
density
adaptive refinement
comparison adaptive - not adaptive
Vijayasundaram Scheme
van-Leer Scheme
pressure
Vijayasundaram Scheme
van-Leer Scheme
Two cylinders in an supersonic flow
grid and adaption efficiency
traceroutes
particle tracing

Scalar Conservation Laws

Linear Transport Equation 1D


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

calculated with

top : leftsided differences

bottom: rightsided differences.

left- and rightsided differences


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

calculated with

top : Lax-Friedrichs-scheme

middle: Lax-Wendroff-scheme

bottom: min-mod limiter scheme.

comparison Lax-Friedrichs, Lax-Wendroff, min-mod Limiter


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

calculated with

top : Lax-Friedrichs-scheme

middle: discontinuous Galerkin scheme

bottom: min-mod limiter scheme.

comparison Lax-Friedrichs, Discontinuous Galerkin, min-mod Limiter


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

calculated with

top : Lax-Wendroff-scheme

middle: Warming & Beam scheme

bottom: min-mod limiter scheme.

comparison Lax-Wendroff, Warming & Beam, min-mod Limiter

Burgers Equation 1D


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

calculated with

top : Lax-Friedrichs-scheme

middle: Engquist-Osher-scheme

bottom: Godunov-scheme.

Comparison Lax-Friedrichs, Engquist-Osher, Godunov (Burgers-Equation)

Systems of Conservation Laws

shocktube

density

adaptive

comparison adaptive - not adaptive

Vijayasundaram-Scheme

van-Leer Scheme

pressure

Vijayasundaram-Scheme

van-Leer Scheme

Two cylinders in a supersonic flow

density

Two cylinders in a supersonic flow (grid and adaption efficiency):

Two cylinders in a supersonic flow (traceroutes):

Two cylinders in a supersonic flow (particle tracing):
Christian Merkle 06/99