2-D sine wave advection test

This test sets up a diagnally travelling sinusoidal density wave, and advects it across the grid, with wrap-around boundaries, back to the initial position. The L1 density norm is used to measure the accuracy of the final conditions comapred to the intial condition. The experiment is repeated by sucessively doubling the resolution of the grid, with the same domain, and the convergence of the result is estimated.

Note: this tests the code's basic advection scheme, not the convergence of the non-linear solution to a Riemann problem.

Compared to the codes tested by L&W, Fyris Alpha performs better or at least as well, with the exception of the original PPM code, which is a truely 3rd order Eulerian method, and the WENO code which is formally 5th order. Fyris compares well with VH1, and unlike CLAW and most of the other central codes, it maintains its convergence degree over all the resolution range.

The code and configuration files plus output for Fyris to run the 2-D advection convergence test will be available soon.

Initial conditions

  • Density = 1.0 +0.2*sin(pi*(x + y))
  • Pressure = 1.000
  • Velocity_x = 1.000, Velocity_y = -0.5

Ending condition

  • Time, t = 2.5

Grid

  • Domain: -1.0 < x <1.0, -1.0 < y < 1.0

  • 25x25 up to 400 x 400 cells.

  • All boundaries are periodic.

Hydrodynamics settings

  • Adiabatic index: Gamma = 1.4

  • CFL number: 0.8 (Standard)

  • Flattening: minimum 0.0, maximum 1.0 (standard)

Results

Scheme
L1, n=25
order
L1, n=50
order
Fyris
4.748E-01
-2.202
1.032E-01
-2.391
CFLFh
2.5
-2.293
5.10E-01
-2.087
JT
1.1
-2.258
2.30E-01
-1.963
LL
2
-1.322
8.00E-01
-1.930
CLAW
4.10E-01
-2.490
7.30E-02
-2.190
WAFT
5.70E-01
0.074
6.00E-01
-1.383
WENO
3.10E-02
-4.998
9.70E-04
-4.968
PPM
2.40E-02
-3.100
2.80E-03
-3.042
VH1
4.50E-01
-2.214
9.70E-02
-2.352
Scheme
L1, n=100
order
L1, n=200
 
L1, n=400
Fyris
1.968E-02
-2.291
4.022E-03
-2.348
7.902E-04
CFLFh
1.20E-01
-1.953
3.10E-02
 
 
JT
5.90E-02
-1.883
1.60E-02
 
 
LL
2.10E-01
-1.959
5.40E-02
 
 
CLAW
1.60E-02
-2.112
3.70E-03
 
 
WAFT
2.30E-01
-1.779
6.70E-02
 
 
WENO
3.10E-05
-4.576
1.30E-06
 
 
PPM
3.40E-04
-2.983
4.30E-05
 
 
VH1
1.90E-02
-2.284
3.90E-03
 
 
 

n = 25, density, auto scaled

 t = 0.0
t = 0.0
 t = 4.0
t = 4.0

 

n= 50, density, auto scaled

 

 t = 0.0
t= 0.0
 t = 4.0
t = 4.0

 

n= 100, density, auto scaled

 

 t = 0.0
t = 0.0
 t = 4.0
t = 4.0

 

n= 200, density, auto scaled

 

 t = 0.0
t= 0.0
 t = 4.0
t = 4.0

 

n= 400, density, auto scaled

 

 t = 0.0
t= 0.0
 t = 4.0
t = 4.0

 

Updated:  19 October 2017/Responsible Officer:  RSAA Director/Page Contact:  Webmaster