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parabolicVelocityProfile.py
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parabolicVelocityProfile.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
""" Copyright, 2018
Xue Li
Calculate the parobolic velocity profile.
"""
import numpy as np
from optimizedParabolicVelocityProfile import OptimizedParabolicVelocityProfile
def ParabolicVelocityProfile(elements, nodes, glbNodeIds, boundary):
""" Calculate the parabolic velocity profile for the inlet.
- elements: elements on the inlet
- nodes: global nodes information
- glbNodeIds: the corresponding global position for each node
return: u, int_u
"""
nNodes = glbNodeIds.shape[0]
K = np.zeros((nNodes, nNodes))
f = np.zeros(nNodes)
Ae = np.zeros(elements.shape[0])
OptimizedParabolicVelocityProfile(nodes, elements, glbNodeIds, K, f, Ae)
# Apply zero velocity at the boundary.
for i in boundary:
K[i,:] = 0.0
K[i,i] = 1.0
f[i] = 0.0
u = np.linalg.solve(K, f)
int_u = np.sum(np.mean(u[elements], axis=1) * Ae)
return u, int_u