/
interpolation_utils.py
167 lines (126 loc) · 4.76 KB
/
interpolation_utils.py
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# flake8: noqa
import numpy as np
def phi1D_lin(xsi):
phi = [1-xsi,
xsi]
return phi
def phi1D_quad(xsi):
phi = [2*xsi**2-3*xsi+1,
-4*xsi**2+4*xsi,
2*xsi**2-xsi]
return phi
def phi2D_lin(xsi, eta):
phi = [(1-xsi) * (1-eta),
xsi * (1-eta),
xsi * eta ,
(1-xsi) * eta ]
return phi
def phi3D_lin(xsi, eta, zet):
phi = [(1-xsi) * (1-eta) * (1-zet),
xsi * (1-eta) * (1-zet),
xsi * eta * (1-zet),
(1-xsi) * eta * (1-zet),
(1-xsi) * (1-eta) * zet ,
xsi * (1-eta) * zet ,
xsi * eta * zet ,
(1-xsi) * eta * zet ]
return phi
def dphidxsi3D_lin(xsi, eta, zet):
dphidxsi = [ - (1-eta) * (1-zet),
(1-eta) * (1-zet),
( eta) * (1-zet),
- ( eta) * (1-zet),
- (1-eta) * ( zet),
(1-eta) * ( zet),
( eta) * ( zet),
- ( eta) * ( zet)]
dphideta = [ - (1-xsi) * (1-zet),
- ( xsi) * (1-zet),
( xsi) * (1-zet),
(1-xsi) * (1-zet),
- (1-xsi) * ( zet),
- ( xsi) * ( zet),
( xsi) * ( zet),
(1-xsi) * ( zet)]
dphidzet = [ - (1-xsi) * (1-eta),
- ( xsi) * (1-eta),
- ( xsi) * ( eta),
- (1-xsi) * ( eta),
(1-xsi) * (1-eta),
( xsi) * (1-eta),
( xsi) * ( eta),
(1-xsi) * ( eta)]
return dphidxsi, dphideta, dphidzet
def dxdxsi3D_lin(hexa_x, hexa_y, hexa_z, xsi, eta, zet, mesh):
dphidxsi, dphideta, dphidzet = dphidxsi3D_lin(xsi, eta, zet)
if mesh == 'spherical':
deg2m = 1852 * 60.
rad = np.pi / 180.
lat = (1-xsi) * (1-eta) * hexa_y[0] + \
xsi * (1-eta) * hexa_y[1] + \
xsi * eta * hexa_y[2] + \
(1-xsi) * eta * hexa_y[3]
jac_lon = deg2m * np.cos(rad * lat)
jac_lat = deg2m
else:
jac_lon = 1
jac_lat = 1
dxdxsi = np.dot(hexa_x, dphidxsi) * jac_lon
dxdeta = np.dot(hexa_x, dphideta) * jac_lon
dxdzet = np.dot(hexa_x, dphidzet) * jac_lon
dydxsi = np.dot(hexa_y, dphidxsi) * jac_lat
dydeta = np.dot(hexa_y, dphideta) * jac_lat
dydzet = np.dot(hexa_y, dphidzet) * jac_lat
dzdxsi = np.dot(hexa_z, dphidxsi)
dzdeta = np.dot(hexa_z, dphideta)
dzdzet = np.dot(hexa_z, dphidzet)
return dxdxsi, dxdeta, dxdzet, dydxsi, dydeta, dydzet, dzdxsi, dzdeta, dzdzet
def jacobian3D_lin(hexa_x, hexa_y, hexa_z, xsi, eta, zet, mesh):
dxdxsi, dxdeta, dxdzet, dydxsi, dydeta, dydzet, dzdxsi, dzdeta, dzdzet = dxdxsi3D_lin(hexa_x, hexa_y, hexa_z, xsi, eta, zet, mesh)
jac = dxdxsi * (dydeta*dzdzet - dzdeta*dydzet)\
- dxdeta * (dydxsi*dzdzet - dzdxsi*dydzet)\
+ dxdzet * (dydxsi*dzdeta - dzdxsi*dydeta)
return jac
def jacobian3D_lin_face(hexa_x, hexa_y, hexa_z, xsi, eta, zet, orientation, mesh):
dxdxsi, dxdeta, dxdzet, dydxsi, dydeta, dydzet, dzdxsi, dzdeta, dzdzet = dxdxsi3D_lin(hexa_x, hexa_y, hexa_z, xsi, eta, zet, mesh)
if orientation == 'zonal':
j = [dydeta*dzdzet-dydzet*dzdeta,
-dxdeta*dzdzet+dxdzet*dzdeta,
dxdeta*dydzet-dxdzet*dydeta]
elif orientation == 'meridional':
j = [dydxsi*dzdzet-dydzet*dzdxsi,
-dxdxsi*dzdzet+dxdzet*dzdxsi,
dxdxsi*dydzet-dxdzet*dydxsi]
elif orientation == 'vertical':
j = [dydxsi*dzdeta-dydeta*dzdxsi,
-dxdxsi*dzdeta+dxdeta*dzdxsi,
dxdxsi*dydeta-dxdeta*dydxsi]
jac = np.sqrt(j[0]**2+j[1]**2+j[2]**2)
return jac
def dphidxsi2D_lin(xsi, eta):
dphidxsi = [-(1-eta),
1-eta,
eta,
- eta]
dphideta = [-(1-xsi),
- xsi,
xsi,
1-xsi]
return dphidxsi, dphideta
def dxdxsi2D_lin(quad_x, quad_y, xsi, eta,):
dphidxsi, dphideta = dphidxsi2D_lin(xsi, eta)
dxdxsi = np.dot(quad_x, dphidxsi)
dxdeta = np.dot(quad_x, dphideta)
dydxsi = np.dot(quad_y, dphidxsi)
dydeta = np.dot(quad_y, dphideta)
return dxdxsi, dxdeta, dydxsi, dydeta
def jacobian2D_lin(quad_x, quad_y, xsi, eta):
dxdxsi, dxdeta, dydxsi, dydeta = dxdxsi2D_lin(quad_x, quad_y, xsi, eta)
jac = dxdxsi*dydeta - dxdeta*dydxsi
return jac
def length2d_lin_edge(quad_x, quad_y, ids):
xe = [quad_x[ids[0]], quad_x[ids[1]]]
ye = [quad_y[ids[0]], quad_y[ids[1]]]
return np.sqrt((xe[1]-xe[0])**2+(ye[1]-ye[0])**2)
def interpolate(phi, f, xsi):
return np.dot(phi(xsi), f)