def steadyStateNewmann(self):
print('running simulation')
# -------------------- Find out size of the complete system -------------------------------------
self.nrCtrlPoints = 0
for i in range(self.nrPanelObjects):
if self.panelObjects[i].liftingSurface:
self.nrCtrlPoints += self.panelObjects[i].mesh.nrFaces + self.panelObjects[i].nrStrips
else:
self.nrCtrlPoints += self.panelObjects[i].mesh.nrFaces
# Global matrix system to solve, A x = b
A = np.zeros((self.nrCtrlPoints, self.nrCtrlPoints))
b = np.zeros(self.nrCtrlPoints)
# -------------------- Build system -------------------------------------------------------------
startTime = time.clock()
i_start = 0
for i in range(self.nrPanelObjects):
# Ctrl points on the surface
pCtrl = self.panelObjects[i].mesh.face_center
nCtrl = self.panelObjects[i].mesh.face_n
nrCtrlPoints = self.panelObjects[i].mesh.nrFaces
# Add kutta ctrl points if ctrl object is a lifting surface
if self.panelObjects[i].liftingSurface:
pCtrl = np.append(pCtrl, self.panelObjects[i].kutta_ctrlPoints, axis=0)
nCtrl = np.append(nCtrl, self.panelObjects[i].kutta_normal, axis=0)
nrCtrlPoints += self.panelObjects[i].nrStrips
i_stop = i_start + nrCtrlPoints
j_start = 0
for j in range(self.nrPanelObjects):
panelObject = self.panelObjects[j]
mesh = self.panelObjects[j].mesh
nrFaces = self.panelObjects[j].mesh.nrFaces
# Number of influence panels
nrInfluence = nrFaces
# Add influence form doublet strips if lifting surface
if self.panelObjects[j].liftingSurface:
nrInfluence += self.panelObjects[j].nrStrips
j_stop = j_start + nrInfluence
A_local = np.zeros((nrCtrlPoints, nrInfluence))
A_local[0:nrCtrlPoints, 0:nrFaces] = Computation.velocityInfluence(pCtrl, nCtrl, mesh, 'source')
# Add contribution from doublet strips if panel object is a lifting surface
if panelObject.liftingSurface:
wake_mesh = self.panelObjects[j].wake_mesh
A_doublet_wake = Computation.velocityInfluence(pCtrl, nCtrl, wake_mesh, 'doublet')
A_doublet_body = Computation.velocityInfluence(pCtrl, nCtrl, mesh, 'doublet')
# Combine result from body and wake into strip based quantities
for k in range(panelObject.nrStrips):
body_stripFaces = self.panelObjects[j].stripFaces[k] # Indices of faces in strip from body
wake_stripFaces = self.panelObjects[j].wake_stripFaces[k] # Indices of faces in strip from wake
stripFaceStrength = self.panelObjects[j].stripFaceStrength[k] # strength value, relative to unknown strip value
A_local[0:nrCtrlPoints, nrFaces + k] = np.sum(A_doublet_body[0:nrCtrlPoints, body_stripFaces]*stripFaceStrength, axis=1)
A_local[0:nrCtrlPoints, nrFaces + k] += np.sum(A_doublet_wake[0:nrCtrlPoints, wake_stripFaces], axis=1)
# Put resulting influence matrix into global matrix
A[i_start:i_stop, j_start:j_stop] = A_local
j_start += nrInfluence
# Compute right side of linear system
b[i_start:i_stop] = Computation.freeStreamNewmann(self.Uinf, nCtrl, nrCtrlPoints)
i_start += nrCtrlPoints
stopTime = time.clock()
print('Matrix assembly time:', stopTime - startTime, 's')
# -------------------- Solve system -------------------------------------------------------------
startTime = time.clock()
strength = np.linalg.solve(A, b)
stopTime = time.clock()
print('Linear solver time:', stopTime - startTime, 's')
# -------------------- Transfer result ----------------------------------------------------------
i_start = 0
for i in range(self.nrPanelObjects):
panelObject = self.panelObjects[i]
i_stop = i_start + panelObject.mesh.nrFaces
panelObject.source_strength = strength[i_start:i_stop]
i_start += panelObject.mesh.nrFaces
if panelObject.liftingSurface:
for j in range(panelObject.nrStrips):
body_stripFaces = panelObject.stripFaces[j] # Indices of faces in strip from body
wake_stripFaces = panelObject.wake_stripFaces[j] # Indices of faces in strip from wake
stripFaceStrength = panelObject.stripFaceStrength[j] # strength value, relative to unknown strip value
panelObject.doublet_strength[body_stripFaces] = strength[i_start + j]*stripFaceStrength
panelObject.wake_strength[wake_stripFaces] = strength[i_start + j]
i_start += panelObject.nrStrips
