ObjectFFRFconvergenceTestHinge.py
You can view and download this file on Github: ObjectFFRFconvergenceTestHinge.py
1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Test for Hurty-Craig-Bampton modes using a simple flexible pendulum meshed with Netgen
5#
6# Author: Johannes Gerstmayr
7# Date: 2021-04-20
8#
9# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
10#
11#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
12
13
14import exudyn as exu
15from exudyn.itemInterface import *
16from exudyn.utilities import *
17from exudyn.FEM import *
18from exudyn.graphicsDataUtilities import *
19import time
20
21SC = exu.SystemContainer()
22mbs = SC.AddSystem()
23
24import numpy as np
25
26#import timeit
27
28import exudyn.basicUtilities as eb
29import exudyn.rigidBodyUtilities as rb
30import exudyn.utilities as eu
31
32import numpy as np
33
34useGraphics = True
35fileName = 'testData/netgenHinge' #for load/save of FEM data
36
37#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
38#netgen/meshing part:
39fem = FEMinterface()
40
41#geometrical parameters:
42L = 0.4 #Length of plate (X)
43w = 0.04 #width of plate (Y)
44h = 0.02 #height of plate (Z)
45d = 0.03 #diameter of bolt
46D = d*2 #diameter of bushing
47b = 0.05 #length of bolt
48nModes = 32 #128
49meshH = 0.01 #0.01 is default, 0.002 gives 100000 nodes and is fairly converged
50#meshH = 0.0014 #203443 nodes, takes 1540 seconds for eigenmode computation (free-free) and 753 seconds for postprocessing on i9
51
52#steel:
53rho = 7850
54Emodulus=2.1e11
55nu=0.3
56
57#test high flexibility
58Emodulus=2e8
59# nModes = 32
60
61
62#helper function for cylinder with netgen
63def CSGcylinder(p0,p1,r):
64 v = VSub(p1,p0)
65 v = Normalize(v)
66 cyl = Cylinder(Pnt(p0[0],p0[1],p0[2]), Pnt(p1[0],p1[1],p1[2]),
67 r) * Plane(Pnt(p0[0],p0[1],p0[2]), Vec(-v[0],-v[1],-v[2])) * Plane(Pnt(p1[0],p1[1],p1[2]), Vec(v[0],v[1],v[2]))
68 return cyl
69
70mBushing = None
71meshCreated = False
72
73#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
74if True: #needs netgen/ngsolve to be installed to compute mesh, see e.g.: https://github.com/NGSolve/ngsolve/releases
75
76 import ngsolve as ngs
77 import netgen
78 from netgen.meshing import *
79
80 from netgen.geom2d import unit_square
81 #import netgen.libngpy as libng
82 from netgen.csg import *
83
84 geo = CSGeometry()
85
86 #plate
87 block = OrthoBrick(Pnt(0, 0, -0.5*h),Pnt(L, w, 0.5*h))
88
89 #bolt
90 bolt0 = CSGcylinder(p0=[0,w,0], p1=[0,0,0], r=1.6*h)
91 bolt = CSGcylinder(p0=[0,0.5*w,0], p1=[0,-b,0], r=0.5*d)
92
93 #bushing
94 bushing = (CSGcylinder(p0=[L,w,0], p1=[L,-b,0], r=0.5*D) -
95 CSGcylinder(p0=[L,0,0], p1=[L,-b*1.1,0], r=0.5*d))
96
97 geo.Add(block+bolt0+bolt+bushing)
98
99 mesh = ngs.Mesh( geo.GenerateMesh(maxh=meshH))
100 mesh.Curve(1)
101
102 if False: #set this to true, if you want to visualize the mesh inside netgen/ngsolve
103 # import netgen
104 import netgen.gui
105 ngs.Draw(mesh)
106 netgen.Redraw()
107
108 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
109 #Use fem to import FEM model and create FFRFreducedOrder object
110 fem.ImportMeshFromNGsolve(mesh, density=rho, youngsModulus=Emodulus, poissonsRatio=nu)
111 meshCreated = True
112 if (meshH==0.01): fem.SaveToFile(fileName)
113
114#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
115#compute Hurty-Craig-Bampton modes
116if True: #now import mesh as mechanical model to EXUDYN
117 if not meshCreated: fem.LoadFromFile(fileName)
118
119 boltP1=[0,0,0]
120 boltP2=[0,-b,0]
121 nodesOnBolt = fem.GetNodesOnCylinder(boltP1, boltP2, radius=0.5*d)
122 #print("boundary nodes bolt=", nodesOnBolt)
123 nodesOnBoltLen = len(nodesOnBolt)
124 nodesOnBoltWeights = np.array((1./nodesOnBoltLen)*np.ones(nodesOnBoltLen))
125
126 bushingP1=[L,0,0]
127 bushingP2=[L,-b,0]
128 nodesOnBushing = fem.GetNodesOnCylinder(bushingP1, bushingP2, radius=0.5*d)
129 #print("boundary nodes bushing=", nodesOnBushing)
130 nodesOnBushingLen = len(nodesOnBushing)
131 nodesOnBushingWeights = np.array((1./nodesOnBushingLen)*np.ones(nodesOnBushingLen))
132
133 print("nNodes=",fem.NumberOfNodes())
134
135 strMode = ''
136 if False: #pure eigenmodes
137 print("compute eigen modes... ")
138 start_time = time.time()
139 fem.ComputeEigenmodes(nModes, excludeRigidBodyModes = 6, useSparseSolver = True)
140 print("eigen modes computation needed %.3f seconds" % (time.time() - start_time))
141 print("eigen freq.=", fem.GetEigenFrequenciesHz())
142
143 elif False:
144 strMode = 'HCB'
145 #boundaryList = [nodesOnBolt, nodesOnBolt, nodesOnBushing] #for visualization, use first interface twice
146 boundaryList = [nodesOnBolt, nodesOnBushing]
147
148 print("compute HCB modes... ")
149 start_time = time.time()
150 fem.ComputeHurtyCraigBamptonModes(boundaryNodesList=boundaryList,
151 nEigenModes=nModes,
152 useSparseSolver=True,
153 computationMode = HCBstaticModeSelection.RBE2)
154
155 print("eigen freq.=", fem.GetEigenFrequenciesHz())
156 print("HCB modes needed %.3f seconds" % (time.time() - start_time))
157 else:
158 strMode = 'HCBsingle'
159 #boundaryList = [nodesOnBolt, nodesOnBolt, nodesOnBushing] #for visualization, use first interface twice
160 boundaryList = [nodesOnBolt]
161
162 print("compute HCB single modes... ")
163 start_time = time.time()
164 fem.ComputeHurtyCraigBamptonModes(boundaryNodesList=boundaryList,
165 nEigenModes=nModes,
166 useSparseSolver=True,
167 computationMode = HCBstaticModeSelection.RBE2)
168
169 print("eigen freq.=", fem.GetEigenFrequenciesHz())
170 print("HCB modes needed %.3f seconds" % (time.time() - start_time))
171
172
173
174 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
175 #compute stress modes for postprocessing (inaccurate for coarse meshes, just for visualization):
176 if False:
177 mat = KirchhoffMaterial(Emodulus, nu, rho)
178 varType = exu.OutputVariableType.StressLocal
179 #varType = exu.OutputVariableType.StrainLocal
180 print("ComputePostProcessingModes ... (may take a while)")
181 start_time = time.time()
182 fem.ComputePostProcessingModes(material=mat,
183 outputVariableType=varType)
184 print(" ... needed %.3f seconds" % (time.time() - start_time))
185 SC.visualizationSettings.contour.reduceRange=False
186 SC.visualizationSettings.contour.outputVariable = varType
187 SC.visualizationSettings.contour.outputVariableComponent = 0 #x-component
188 else:
189 SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.DisplacementLocal
190 SC.visualizationSettings.contour.outputVariableComponent = -1
191
192 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
193 print("create CMS element ...")
194 cms = ObjectFFRFreducedOrderInterface(fem)
195
196 objFFRF = cms.AddObjectFFRFreducedOrder(mbs, positionRef=[0,0,0],
197 initialVelocity=[0,0,0],
198 initialAngularVelocity=[0,0,0],
199 color=[0.9,0.9,0.9,1.],
200 )
201
202 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
203 #add markers and joints
204 nodeDrawSize = 0.0025 #for joint drawing
205
206
207 #mRB = mbs.AddMarker(MarkerNodeRigid(nodeNumber=objFFRF['nRigidBody']))
208
209 if False:
210 boltMidPoint = 0.5*(np.array(boltP1)+boltP2)
211
212 oGround = mbs.AddObject(ObjectGround(referencePosition= [0,0,0]))
213
214 altApproach = True
215 mBolt = mbs.AddMarker(MarkerSuperElementRigid(bodyNumber=objFFRF['oFFRFreducedOrder'],
216 meshNodeNumbers=np.array(nodesOnBolt), #these are the meshNodeNumbers
217 #referencePosition=boltMidPoint,
218 useAlternativeApproach=altApproach,
219 weightingFactors=nodesOnBoltWeights))
220 bushingMidPoint = 0.5*(np.array(bushingP1)+bushingP2)
221
222 #add marker for visualization of boundary nodes
223 mBushing = mbs.AddMarker(MarkerSuperElementRigid(bodyNumber=objFFRF['oFFRFreducedOrder'],
224 meshNodeNumbers=np.array(nodesOnBushing), #these are the meshNodeNumbers
225 #referencePosition=bushingMidPoint,
226 useAlternativeApproach=altApproach,
227 weightingFactors=nodesOnBushingWeights))
228
229 lockedAxes=[1,1,1,1,1*0,1]
230 if True:
231
232 mGroundBolt = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround,
233 localPosition=boltMidPoint,
234 visualization=VMarkerBodyRigid(show=True)))
235 mbs.AddObject(GenericJoint(markerNumbers=[mGroundBolt, mBolt],
236 constrainedAxes = lockedAxes,
237 visualization=VGenericJoint(show=False, axesRadius=0.1*b, axesLength=0.1*b)))
238
239 else:
240
241 mGroundBushing = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=bushingMidPoint))
242 mbs.AddObject(GenericJoint(markerNumbers=[mGroundBushing, mBushing],
243 constrainedAxes = lockedAxes,
244 visualization=VGenericJoint(axesRadius=0.1*b, axesLength=0.1*b)))
245
246
247 if False:
248 cms = ObjectFFRFreducedOrderInterface(fem)
249
250 objFFRF = cms.AddObjectFFRFreducedOrder(mbs, positionRef=[0,0,0],
251 initialVelocity=[990,990,990],
252 initialAngularVelocity=[0,0,0],
253 color=[0.9,0.9,0.9,1.],
254 )
255
256 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
257 #animate modes
258 SC.visualizationSettings.markers.show = True
259 SC.visualizationSettings.markers.defaultSize=0.0075
260 SC.visualizationSettings.markers.drawSimplified = False
261
262 SC.visualizationSettings.loads.show = False
263 SC.visualizationSettings.loads.drawSimplified = False
264 SC.visualizationSettings.loads.defaultSize=0.1
265 SC.visualizationSettings.loads.defaultRadius = 0.002
266
267 SC.visualizationSettings.openGL.multiSampling=4
268 SC.visualizationSettings.openGL.lineWidth=2
269
270 if False: #activate to animate modes
271 from exudyn.interactive import AnimateModes
272 mbs.Assemble()
273 SC.visualizationSettings.nodes.show = False
274 SC.visualizationSettings.openGL.showFaceEdges = True
275 SC.visualizationSettings.openGL.multiSampling=4
276 SC.visualizationSettings.openGL.lineWidth=2
277 SC.visualizationSettings.window.renderWindowSize = [1600,1080]
278 SC.visualizationSettings.contour.showColorBar = False
279 SC.visualizationSettings.general.textSize = 16
280
281 #%%+++++++++++++++++++++++++++++++++++++++
282 #animate modes of ObjectFFRFreducedOrder (only needs generic node containing modal coordinates)
283 SC.visualizationSettings.general.autoFitScene = False #otherwise, model may be difficult to be moved
284
285 nodeNumber = objFFRF['nGenericODE2'] #this is the node with the generalized coordinates
286 AnimateModes(SC, mbs, nodeNumber, period=0.1, showTime=False, renderWindowText='Hurty-Craig-Bampton: 2 x 6 static modes and 8 eigenmodes\n')
287 # import sys
288 # sys.exit()
289
290 #add gravity (not necessary if user functions used)
291 oFFRF = objFFRF['oFFRFreducedOrder']
292 mBody = mbs.AddMarker(MarkerBodyMass(bodyNumber=oFFRF))
293 mbs.AddLoad(LoadMassProportional(markerNumber=mBody, loadVector= [0,0,-9.81*0]))
294
295
296 #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
297 if mBushing != None:
298 fileDir = 'solution/'
299 # sensBolt = mbs.AddSensor(SensorMarker(markerNumber=mBolt,
300 # fileName=fileDir+'hingePartBoltPos'+str(nModes)+strMode+'.txt',
301 # outputVariableType = exu.OutputVariableType.Position))
302 # sensBushing= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
303 # fileName=fileDir+'hingePartBushingPos'+str(nModes)+strMode+'.txt',
304 # outputVariableType = exu.OutputVariableType.Position))
305 sensBushingVel= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
306 fileName=fileDir+'hingePartBushingVel'+str(nModes)+strMode+'.txt',
307 outputVariableType = exu.OutputVariableType.Velocity))
308 sensBushing= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
309 fileName=fileDir+'hingePartBushing'+str(nModes)+strMode+'.txt',
310 outputVariableType = exu.OutputVariableType.Position))
311
312 mbs.Assemble()
313
314 simulationSettings = exu.SimulationSettings()
315
316 SC.visualizationSettings.nodes.defaultSize = nodeDrawSize
317 SC.visualizationSettings.nodes.drawNodesAsPoint = False
318 SC.visualizationSettings.connectors.defaultSize = 2*nodeDrawSize
319
320 SC.visualizationSettings.nodes.show = False
321 SC.visualizationSettings.nodes.showBasis = True #of rigid body node of reference frame
322 SC.visualizationSettings.nodes.basisSize = 0.12
323 SC.visualizationSettings.bodies.deformationScaleFactor = 1 #use this factor to scale the deformation of modes
324
325 SC.visualizationSettings.openGL.showFaceEdges = True
326 SC.visualizationSettings.openGL.showFaces = True
327
328 SC.visualizationSettings.sensors.show = True
329 SC.visualizationSettings.sensors.drawSimplified = False
330 SC.visualizationSettings.sensors.defaultSize = 0.01
331
332
333 simulationSettings.solutionSettings.solutionInformation = "CMStutorial "+str(nModes)+" "+strMode+"modes"
334
335 h=0.25e-3
336 tEnd = 1
337
338 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
339 simulationSettings.timeIntegration.endTime = tEnd
340 simulationSettings.solutionSettings.writeSolutionToFile = False
341 simulationSettings.timeIntegration.verboseMode = 1
342 #simulationSettings.timeIntegration.verboseModeFile = 3
343 simulationSettings.timeIntegration.newton.useModifiedNewton = True
344
345 simulationSettings.solutionSettings.sensorsWritePeriod = h
346
347 simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8
348 #simulationSettings.displayStatistics = True
349 simulationSettings.displayComputationTime = True
350
351 #create animation:
352 # simulationSettings.solutionSettings.recordImagesInterval = 0.005
353 # SC.visualizationSettings.exportImages.saveImageFileName = "animation/frame"
354 SC.visualizationSettings.window.renderWindowSize=[1920,1080]
355 SC.visualizationSettings.openGL.multiSampling = 4
356
357 if True:
358 if useGraphics:
359 SC.visualizationSettings.general.autoFitScene=False
360
361 exu.StartRenderer()
362 if 'renderState' in exu.sys: SC.SetRenderState(exu.sys['renderState']) #load last model view
363
364 mbs.WaitForUserToContinue() #press space to continue
365
366 #SC.RedrawAndSaveImage()
367 if True:
368 # mbs.SolveDynamic(solverType=exu.DynamicSolverType.TrapezoidalIndex2,
369 # simulationSettings=simulationSettings)
370 mbs.SolveDynamic(simulationSettings=simulationSettings)
371 else:
372 mbs.SolveStatic(simulationSettings=simulationSettings)
373
374
375 if useGraphics:
376 SC.WaitForRenderEngineStopFlag()
377 exu.StopRenderer() #safely close rendering window!
378
379 if mBushing != None:
380 uTip = mbs.GetSensorValues(sensBushing)
381 print("nModes="+strMode, nModes, ", bushing position=", uTip)
382 if False:
383
384 mbs.PlotSensor(sensorNumbers=[sensBushingVel], components=[1])
385
386#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
387if True:
388 import matplotlib.pyplot as plt
389 import matplotlib.ticker as ticker
390 import exudyn as exu
391 from exudyn.utilities import *
392 CC = PlotLineCode
393 comp = 3 #1=x, 2=y, ...
394 var = 'Vel'
395 # data = np.loadtxt('solution/hingePartBushing'+var+'2.txt', comments='#', delimiter=',')
396 # plt.plot(data[:,0], data[:,comp], CC(7), label='2 eigenmodes')
397 # data = np.loadtxt('solution/hingePartBushing'+var+'4.txt', comments='#', delimiter=',')
398 # plt.plot(data[:,0], data[:,comp], CC(8), label='4 eigenmodes')
399 data = np.loadtxt('solution/hingePartBushing'+var+'8.txt', comments='#', delimiter=',')
400 plt.plot(data[:,0], data[:,comp], CC(8), label='8 eigenmodes')
401 data = np.loadtxt('solution/hingePartBushing'+var+'16.txt', comments='#', delimiter=',')
402 plt.plot(data[:,0], data[:,comp], CC(9), label='16 eigenmodes')
403 data = np.loadtxt('solution/hingePartBushing'+var+'32.txt', comments='#', delimiter=',')
404 plt.plot(data[:,0], data[:,comp], CC(10), label='32 eigenmodes')
405 data = np.loadtxt('solution/hingePartBushing'+var+'64.txt', comments='#', delimiter=',')
406 plt.plot(data[:,0], data[:,comp], CC(11), label='64 eigenmodes')
407 data = np.loadtxt('solution/hingePartBushing'+var+'64.txt', comments='#', delimiter=',')
408 plt.plot(data[:,0], data[:,comp], CC(12), label='64 eigenmodes')
409 data = np.loadtxt('solution/hingePartBushing'+var+'128.txt', comments='#', delimiter=',')
410 plt.plot(data[:,0], data[:,comp], CC(13), label='128 eigenmodes')
411
412 # data = np.loadtxt('solution/hingePartBushing'+var+'2HCB.txt', comments='#', delimiter=',')
413 # plt.plot(data[:,0], data[:,comp], CC(1), label='HCB + 2 eigenmodes')
414 data = np.loadtxt('solution/hingePartBushing'+var+'4HCB.txt', comments='#', delimiter=',')
415 plt.plot(data[:,0], data[:,comp], CC(2), label='HCB2 + 4 eigenmodes')
416 data = np.loadtxt('solution/hingePartBushing'+var+'8HCB.txt', comments='#', delimiter=',')
417 plt.plot(data[:,0], data[:,comp], CC(3), label='HCB2 + 8 eigenmodes')
418 data = np.loadtxt('solution/hingePartBushing'+var+'16HCB.txt', comments='#', delimiter=',')
419 plt.plot(data[:,0], data[:,comp], CC(4), label='HCB2 + 16 eigenmodes')
420 data = np.loadtxt('solution/hingePartBushing'+var+'32HCB.txt', comments='#', delimiter=',')
421 plt.plot(data[:,0], data[:,comp], CC(5), label='HCB2 + 32 eigenmodes')
422 data = np.loadtxt('solution/hingePartBushing'+var+'64HCB.txt', comments='#', delimiter=',')
423 plt.plot(data[:,0], data[:,comp], CC(6), label='HCB2 + 64 eigenmodes')
424 data = np.loadtxt('solution/hingePartBushing'+var+'128HCB.txt', comments='#', delimiter=',')
425 plt.plot(data[:,0], data[:,comp], CC(7), label='HCB2 + 128 eigenmodes')
426
427 data = np.loadtxt('solution/hingePartBushing'+var+'2HCBsingle.txt', comments='#', delimiter=',')
428 plt.plot(data[:,0], data[:,comp], CC(14), label='HCB1 + 2 eigenmodes')
429 data = np.loadtxt('solution/hingePartBushing'+var+'4HCBsingle.txt', comments='#', delimiter=',')
430 plt.plot(data[:,0], data[:,comp], CC(15), label='HCB1 + 4 eigenmodes')
431 data = np.loadtxt('solution/hingePartBushing'+var+'8HCBsingle.txt', comments='#', delimiter=',')
432 plt.plot(data[:,0], data[:,comp], CC(16), label='HCB1 + 8 eigenmodes')
433 data = np.loadtxt('solution/hingePartBushing'+var+'16HCBsingle.txt', comments='#', delimiter=',')
434 plt.plot(data[:,0], data[:,comp], CC(17), label='HCB1 + 16 eigenmodes')
435 data = np.loadtxt('solution/hingePartBushing'+var+'32HCBsingle.txt', comments='#', delimiter=',')
436 plt.plot(data[:,0], data[:,comp], CC(18), label='HCB1 + 32 eigenmodes')
437 data = np.loadtxt('solution/hingePartBushing'+var+'64HCBsingle.txt', comments='#', delimiter=',')
438 plt.plot(data[:,0], data[:,comp], CC(19), label='HCB1 + 64 eigenmodes')
439 data = np.loadtxt('solution/hingePartBushing'+var+'128HCBsingle.txt', comments='#', delimiter=',')
440 plt.plot(data[:,0], data[:,comp], CC(20), label='HCB1 + 128 eigenmodes')
441
442
443 ax=plt.gca() # get current axes
444 ax.grid(True, 'major', 'both')
445 ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
446 ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
447 #
448 plt.xlabel("time (s)")
449 plt.ylabel("y-component of tip velocity of hinge (m)")
450 plt.legend() #show labels as legend
451 plt.tight_layout()
452 plt.show()
453
454#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
455if True:
456 varList = ['','HCB','HCBsingle']
457 for var in varList:
458 for i in range(6):
459 n = 4*2**i
460 filename = 'solution/hingePartBushingVel'+str(n)+var+'.txt'
461 #print(filename)
462 data = np.loadtxt(filename, comments='#', delimiter=',')
463 s = var + " eigenmodes"
464 print("solution with "+str(n)+" "+s+" = ",data[-1,1],", ",data[-1,2],", ",data[-1,3],sep="")
465
466#++++++++++++++++++++++
467#(x,y,z-position results for h=0.25e-3, tEnd = 1:
468# solution with 4 eigenmodes = -0.1218716941, -0.02212539352, -0.3826646827
469# solution with 8 eigenmodes = -0.1246493313, -0.02134551124, -0.3817672439
470# solution with 16 eigenmodes = -0.125718746, -0.02220973667, -0.3817761998
471# solution with 32 eigenmodes = -0.1227923675, -0.02232804332, -0.3826703705
472# solution with 64 eigenmodes = -0.1211624347, -0.02256801385, -0.3830241186
473# solution with 128 eigenmodes = -0.1211098342, -0.02258891649, -0.3830239774
474
475# solution with 4 HCB eigenmodes = -0.137803822, -0.02140481771, -0.377325894
476# solution with 8 HCB eigenmodes = -0.09278682737, -0.02088216306, -0.3910735225
477# solution with 16 HCB eigenmodes = -0.1006048749, -0.0210529449, -0.3890880585
478# solution with 32 HCB eigenmodes = -0.1418260115, -0.02137465745, -0.3755985975
479# solution with 64 HCB eigenmodes = -0.1261576272, -0.02133676138, -0.3811615539
480# solution with 128 HCB eigenmodes = -0.1249497117, -0.02134015915, -0.381582143
481
482# solution with 4 HCBsingle eigenmodes = -0.1236432594, -0.02127703127, -0.3822381713
483# solution with 8 HCBsingle eigenmodes = -0.1553884175, -0.02144366871, -0.3712096711
484# solution with 16 HCBsingle eigenmodes = -0.1096747619, -0.02127260753, -0.3871797944
485# solution with 32 HCBsingle eigenmodes = -0.130126813, -0.02149842833, -0.3807721171
486# solution with 64 HCBsingle eigenmodes = -0.1261109915, -0.02147756767, -0.3821287225
487# solution with 128 HCBsingle eigenmodes = -0.1269092416, -0.02148461514, -0.3818634658
488
489#NOTE: main differences due to different initial conditions (USE offset, bad convergence of HCB modes for gravity, etc.)
490#(x,y,z-velocity results for h=0.25e-3, tEnd = 1:
491# solution with 4 eigenmodes = 2.798215342, 0.0123889876, -0.894408541
492# solution with 8 eigenmodes = 2.753795922, 0.001046355507, -1.033353889
493# solution with 16 eigenmodes = 2.862677224, 0.05041922189, -0.70615996
494# solution with 32 eigenmodes = 2.886092992, 0.04990608422, -0.783893511
495# solution with 64 eigenmodes = 2.82897851, -0.02284196211, -0.9656913985
496# solution with 128 eigenmodes = 2.839233628, 0.001567636751, -0.9556805815
497#
498# solution with 4 HCB eigenmodes = 2.841690471, 0.02171168723, -0.8530592818
499# solution with 8 HCB eigenmodes = 2.96737056, -0.01208003067, -0.6819585453
500# solution with 16 HCB eigenmodes = 2.919615786, -0.01640113107, -0.7205707584
501# solution with 32 HCB eigenmodes = 2.803855522, 0.01284070602, -0.9694702614
502# solution with 64 HCB eigenmodes = 2.86587674, 0.01787123237, -0.8448990047
503# solution with 128 HCB eigenmodes = 2.87133748, 0.03213267314, -0.8176578849
504#
505# solution with 4 HCBsingle eigenmodes = 2.790998662, 0.007480706365, -0.9071953092
506# solution with 8 HCBsingle eigenmodes = 2.71735531, 0.005031127492, -1.102723094
507# solution with 16 HCBsingle eigenmodes = 2.889954015, -0.005524615368, -0.8508318815
508# solution with 32 HCBsingle eigenmodes = 2.856518668, 0.03496577193, -0.8353875884
509# solution with 64 HCBsingle eigenmodes = 2.867595936, 0.03403208487, -0.8067800302
510# solution with 128 HCBsingle eigenmodes = 2.865221368, 0.03422539291, -0.8118038999