2D sine wave advection test
This test sets up a diagnally travelling sinusoidal density wave, and advects it across the grid, with wraparound 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 nonlinear 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 2D 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

4.748E01

2.202

1.032E01

2.391

CFLFh

2.5

2.293

5.10E01

2.087

JT

1.1

2.258

2.30E01

1.963

LL

2

1.322

8.00E01

1.930

CLAW

4.10E01

2.490

7.30E02

2.190

WAFT

5.70E01

0.074

6.00E01

1.383

WENO

3.10E02

4.998

9.70E04

4.968

PPM

2.40E02

3.100

2.80E03

3.042

VH1

4.50E01

2.214

9.70E02

2.352

Scheme

L1, n=100

order

L1, n=200


L1, n=400


Fyris

1.968E02

2.291

4.022E03

2.348

7.902E04

CFLFh

1.20E01

1.953

3.10E02



JT

5.90E02

1.883

1.60E02



LL

2.10E01

1.959

5.40E02



CLAW

1.60E02

2.112

3.70E03



WAFT

2.30E01

1.779

6.70E02



WENO

3.10E05

4.576

1.30E06



PPM

3.40E04

2.983

4.30E05



VH1

1.90E02

2.284

3.90E03



n = 25, density, auto scaled
n= 50, density, auto scaled
n= 100, density, auto scaled
n= 200, density, auto scaled
n= 400, density, auto scaled