Fyris Alpha - 2D Gresho Vortex Test

2D Gresho Vortex Tests

The Gresho vortex is a 2D pattern where the cetrifugal force are matched by pressure gradients, resulting in a stable time-independent vortex.

This 2D L&W test consists of single 2D vortex on a range of grid resolutions. One test models a stationary vortex, and the second test advects the vortex across three diameters.

The code and configuration files plus output for Fyris to run the 2D Advection Convergence Test will be available soon.

The vortex is defined here by:

Initial Conditions

A vortex initially centred about (0.5, 0.5), outer radius r = 0.40

Adiabatic index Gamma = 5/3

Density = 1.0 everywhere

Pressure:

r <= 0.2; P(r) = 5.0 +25/2 r^2
0.2 < r <= 0.4 ; 9 – 4 ln 0.2 + 25/2 r^2 – 20 r + 4 ln r,
0.4 < r ; 3 + 4 ln 2

Azimuthal Velocity v_phi:

r <= 0.2; v_phi(r) = 5r
0.2 < r <= 0.4 ; v_phi(r) = 2 – 5r,
0.4 < r ; v_phi(r) = 0.0

The resulting 2D vorticity, V_yx (r), is

r <= 0.2; V_yx(r) = 10.0
0.2 < r <= 0.4 ; V_yx(r) = 2/r - 10.0
0.4 < r ; V_yx(r) = 0.0

The Stationary Vortex

Ending Condition:

Time, t = 3.0

Grid:

Domain: x = 0 -> 1.0, , y = 0 -> 1.0,
Boundary conditions are free or natural boundaries.
Runs are made on a 20x20 (a20), 40x40 (a40), 60x60 (a60) and 80x80 (a80) grid.

Hydrodynamics Settings:

CFL number: 0.8, initial step 0.4 (standard)
Flattening: minimum 0.0, maximum 1.0 (standard)

Errors and L1 norms are computed over a unit square centred on (0.5, 0.5) at t = 3.0.

The Stationary Vortex at t = 3.0

Stationary	Density L1 %				Vorticity L1 %				Total KE Error %
Code	a20	a40	a60	a80	a20	a40	a60	a80	a20	a40	a60	a80
Fyris	0.150	0.0276	0.0181	0.0144	26.4	14.5	11.1	8.89	11.6	1.85	0.733	0.383
CFLFh	0.22	0.16			22	20			0.2	0.4
JT	0.56	0.22			89	45			55.2	18.3
LL	2.27	0.23			71	44			65.6	26.1
CLAW	0.33	0.10			50	28			29.9	6.1
WAFT	0.24	0.07			47	26			7.7	5.7
WENO	0.35	0.06			38	27			30.9	3.7
PPM	0.20	0.04			25	13			9.1	0.8
VH1	0.15	0.04			26	15			9.6	1.2


a20 Density (0.996072, 1.00688)	a20 Pressure (5.05753, 5.79528)	a20 Vorticity (-4.19047, 11.0509)	a20 Velocity_x (-0.795881, 0.795881)

a40 Density (0.998955, 1.00132)	a40 Pressure (5.01343, 5.77697)	a40 Vorticity (-4.45904, 10.4167)	a40 Velocity_x (-0.899295, 0.899295)

a60 Density (0.999382, 1.00105)	a60 Pressure (5.00564, 5.77629)	a60 Vorticity (-4.92575, 10.3582)	a60 Velocity_x (-0.928645, 0.928645)

a80 Density (0.999134, 1.00096)	a80 Pressure (5.00309, 5.77541)	a80 Vorticity (-5.19555 , 10.3471)	a80 Velocity_x (-0.941055, 0.941055)
(minmax)

The Moving Vortex

Same as the stationary vortex, with a global v_x = 1.0 drift velocity added to the whole grid, on top of the initial vortex velocity field.

Ending Condition:

Time, t = 3.0

Grid:

Domain:0.0 < x < 4.0, 0.0 < y <1.0
Boundary conditions are free or natural boundaries.
Runs are made on a 20x80 (b20), 40x160 (b40), 60x240 (b60) and 80x320 (b80) grid.

The vortex drifts from the left to the right. At t = 3.0 the vortex should be centred on (3.5,0.5).

Errors and L1 norms are computed over a unit square centred on the expected vortex centre at t = 3.0.

Results

The vorticity is estimated from the discrete grid by the central finite difference:

vorticity[i,j] = 0.5*{(vy[i+1, j]-vy[i-1,j])/dx - (vx[i, j+1]-vx[i,j-1])/dy}

Moving Vortex at t = 3.0

Stationary	Density L1 %				Vorticity L1 %				Total KE Error %
Code	b20	b40	b60	b80	b20	b40	b60	b80	b20	b40	b60	b80
Fyris	0.649	0.568	0.104	0.042	62.08	56.47	18.97	14.52	2.072	0.031	0.039	0.003
CFLFh	1.12	0.72			145	83			12.8	0.1
JT	0.81	0.22			100	52			42.8	22.1
LL	0.65	0.49			88	60			71.6	30.9
CLAW	0.72	0.29			65	37			39.9	8.3
WAFT	0.87	0.77			65	62			1.3	12.6
WENO	0.37	0.43			48	40			31.6	4.0
PPM	1.1	0.42			93	36			4.9	1.0
VH1	0.8	0.66			65	55			11.7	1.2


b20 Density (0.980141, 1.02896)	b20 Pressure (5.17565 , 5.8355)	b20 Vorticity (-4.46422, 16.7204)	b20 Velocity_x (0.140607, 1.86165)

b40 Density ( 0.977118, 1.01814)	b40 Pressure (5.1033, 5.81134)	b40 Vorticity (-5.56746, 11.4596)	b40 Velocity_x (0.34762, 1.6984)

b60 Density (0.995089, 1.00389)	b60 Pressure (5.00907, 5.78504)	b60 Vorticity (-5.23023, 11.0323)	b60 Velocity_x (0.0961467, 1.90601)

b80 Density (0.997859, 1.00166)	b80 Pressure (5.00332, 5.78039)	b80 Vorticity (-5.1049 , 10.974)	b80 Velocity_x (0.0770731, 1.9277)
(minmax)

Skip Navigation \| ANU Home \| Search ANU \| Directories
	Research School of Astronomy and Astrophysics Fyris Alpha Simulation Code