This page presents some examples of mesh adaptation using pyAMG.
These examples require to have the pyAMG/SU2 interface installed.
This simple 3D example consists in reading an initial mesh of a cube, adapting it using a smaller specified edge size, and writing the final adapted mesh.
Download: cube.meshb (the initial mesh)
import pyamg, math, numpy as np
# Define maximal edge size
remesh_options = {}
remesh_options['hmax'] = 0.1
# Read initial mesh
msh3d = pyamg.read_mesh("cube.meshb")
msh3d_unif = pyamg.adapt_mesh(msh3d, remesh_options)
# Output refined mesh
pyamg.write_mesh(msh3d_unif,"cube_unif.meshb")
Initial mesh and uniformely refined mesh.
In this example, an initial mesh of a cube is loaded and an anisotropic analytical function is computed at each of its nodes.
Download: cube.meshb (the initial mesh)
import pyamg, math, numpy as np
def analytical_fun(x,y,z=1):
xyz = (x-0.4)*(y-0.4)*(z-0.4)
if( xyz <= (-1.*math.pi/50.)): return 0.1*math.sin(50.*xyz)
elif(xyz <= 2.*math.pi/50.): return math.sin(50.*xyz)
else: return 0.1*math.sin(50.*xyz)
def create_sensor(mesh):
sensor = []
crd = []
if ( 'xyz' in mesh ):
crd = mesh['xyz']
for x in crd:
sensor.append(analytical_fun(x[0],x[1],x[2]))
elif ( 'xy' in mesh ):
crd = mesh['xy']
for x in crd:
sensor.append(analytical_fun(x[0],x[1]))
return sensor
# Load mesh
msh3d = pyamg.read_mesh("cube.meshb")
# Create the sensor for adaptation
msh3d['sensor'] = create_sensor(msh3d)
Then, the 'Lp' remeshing option is set such that the
interpolation error of the sensor will be controled in L^2 norm. Five adaptive iterations are
performed to capture the anisotropy, and the final mesh is outputted.
# Define remeshing options
remesh_options = {}
remesh_options['Lp'] = 2
remesh_options['gradation'] = 1.5
remesh_options['target'] = 20000
# Adapt the mesh, perform 5 iterations
print " Anisotropic adaptation : iteration 1"
msh3d_aniso = pyamg.adapt_mesh(msh3d, remesh_options)
for ite in range(2,5):
print " Anisotropic adaptation : iteration %d " %(ite)
msh3d_aniso['sensor'] = create_sensor(msh3d_aniso)
msh3d_aniso = pyamg.adapt_mesh(msh3d_aniso, remesh_options)
# Output final mesh
pyamg.write_mesh(msh3d_aniso,"cube_aniso.meshb")
Initial mesh and adapted mesh using a control of the interpolation error.
Here, an isotropic refinement using a sizing field is shown. This is done using the key "Metric" in the mesh data
structure. We illustrate this through the refinement around the corner (0,0,0) of the unit cube.
Download: cube.meshb (the initial mesh)
We start by defining the sizing function.
import pyamg, math, numpy as np
def analytical_sizing(x,y,z=1):
d = math.sqrt(x*x + y*y + z*z)
hmin = 0.01
hmed = 0.1
hmax = 0.5
if ( d <= 10*hmin ): return hmin
elif( d <= 10*hmin+ 5*hmed ): return hmed
else: return hmax
def create_sizing(mesh):
size = []
crd = []
if ( 'xyz' in mesh ):
crd = mesh['xyz']
for x in crd:
size.append(analytical_sizing(x[0],x[1],x[2]))
elif ( 'xy' in mesh ):
size.append(0.2)
return size
# Load mesh
msh3d = pyamg.read_mesh("cube.meshb")
Five adaptive steps are then performed to generate the final mesh. The error is controlled in L2 norm.
# Define remeshing options
remesh_options = {}
remesh_options['gradation'] = 1.5
remesh_options['logfile'] = "remesh-adap-metric.log"
msh3d.pop('sensor',None)
msh3d['metric'] = create_sizing(msh3d)
print " Adaptation : iteration 1"
msh3d_iso = pyamg.adapt_mesh(msh3d, remesh_options)
for ite in range(2,5):
print " Adaptation : iteration %d " %(ite)
msh3d_iso['metric'] = create_sizing(msh3d_iso)
msh3d_iso = pyamg.adapt_mesh(msh3d_iso, remesh_options)
print "\n output : cube_iso.meshb \n"
pyamg.write_mesh(msh3d_iso,"cube_iso.meshb")
Initial mesh and refined mesh using an isotropic sizing function.
Note: This example requires to have the pyAMG/SU2 interface installed.
The following files are required:
This example uses the geometry and the flow conditions of the Inviscid ONERA M6 SU2 test case.
The goal of this mesh adaptation is to accurately capture the shocks around the airfoil, by creating anisotropic mesh elements along the shocks' directions of anisotropy. The Mach number is used as the sensor for mesh adaptation.
% ------------- MESH ADAPTATION PARAMETER ------------%
% Mesh size parameters
ADAP_SIZES= (100, 200, 300)
% Number of iterative loops performed for each mesh size
ADAP_SUBITE= (2, 2, 2)
% Number of CFD iterations for each mesh size
ADAP_EXT_ITER= (500, 500, 500)
% Prescribed residual reduction for each mesh size
ADAP_RESIDUAL_REDUCTION= (3, 3, 3)
% Sensor used for mesh adaptation
% (MACH, PRES, or MACH_PRES)
ADAP_SENSOR= MACH
% Max and min edge sizes
ADAP_HMAX= 200
ADAP_HMIN= 1e-8
% Prescribed mesh gradation
ADAP_HGRAD= 1.3
% Output adapted mesh
MESH_OUT_FILENAME= mesh_NACA0012_adap.su2
% Final adapted restart solution
RESTART_FLOW_FILENAME= NACA0012_adap.dat
% Initial restart solution
SOLUTION_FLOW_FILENAME= NACA0012_ini.datThe mesh adaptation process is started by running the following command line in a terminal:
$ mesh_adaptation_amg.py -f adap_NACA0012.cfg -n 4-n option corresponds to the desired number of
processing cores.
A ./ADAP folder is created, in which the successive calls to
SU2_CFD and pyAMG are performed. Once all the adaptive iterations are done, the final adapted mesh
and restart solution are outputted in the current directory.
A comparison of the initial and final meshes/solutions is shown in the figures below.
Note: This example requires to have the pyAMG/SU2 interface installed.
The following files are required:
This example uses the geometry and the flow conditions of the Inviscid ONERA M6 SU2 test case.
The goal of this mesh adaptation is to accurately capture the typical "lambda" shock along the upper surface of the lifting wing, by creating anisotropic mesh elements along the shock's directions of anisotropy. The Mach number is used as the sensor for mesh adaptation.
% -- MESH ADAPTATION PARAMETER --%
% Mesh size parameters
ADAP_SIZES= (2000, 4000, 8000)
% Number of iterative loops performed for each mesh size
ADAP_SUBITE= (2, 2, 2)
% Number of CFD iterations for each mesh size
ADAP_EXT_ITER= (1000, 1000, 1000)
% Prescribed residual reduction for each mesh size
ADAP_RESIDUAL_REDUCTION= (3, 3, 3)
% Sensor used for mesh adaptation
% (MACH, PRES, or MACH_PRES)
ADAP_SENSOR= MACH
% Max and min edge sizes
ADAP_HMAX= 200
ADAP_HMIN= 1e-8
% Prescribed mesh gradation
ADAP_HGRAD= 1.3
% Output adapted mesh
MESH_OUT_FILENAME= M6_adap.su2
% Final adapted restart solution
RESTART_FLOW_FILENAME= M6_adap.datThe mesh adaptation process is started by running the following command line in a terminal:
$ mesh_adaptation_amg.py -f adap_ONERAM6.cfg -n 4-n option corresponds to the desired number of
processing cores.
A ./ADAP folder is created, in which the successive calls to
SU2_CFD and pyAMG are performed. Once all the adaptive iterations are done, the final adapted mesh
and restart solution are outputted in the current directory.
A comparison of the initial and final meshes/solutions is shown in the figure below. The lambda shock resolution is improved, while reducing the number of mesh vertices.
