Nektar++
BetaPressureArea.cpp
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3 // File: BetaPressureArea.cpp
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31 //
32 // Description: BetaPressureArea class
33 //
34 ///////////////////////////////////////////////////////////////////////////////
35 
36 #include <PulseWaveSolver/EquationSystems/BetaPressureArea.h>
37 
38 using namespace std;
39 
40 namespace Nektar
41 {
42 
43 std::string BetaPressureArea::className =
44  GetPressureAreaFactory().RegisterCreatorFunction(
45  "Beta", BetaPressureArea::create,
46  "Beta law pressure area relationship for the arterial system");
47 
48 BetaPressureArea::BetaPressureArea(
49  Array<OneD, MultiRegions::ExpListSharedPtr> pVessel,
50  const LibUtilities::SessionReaderSharedPtr pSession)
51  : PulseWavePressureArea(pVessel, pSession)
52 {
53 }
54 
55 BetaPressureArea::~BetaPressureArea()
56 {
57 }
58 
59 void BetaPressureArea::v_GetPressure(NekDouble &P, const NekDouble &beta,
60  const NekDouble &A, const NekDouble &A0,
61  const NekDouble &dAUdx,
62  const NekDouble &gamma,
63  const NekDouble &alpha)
64 {
65  boost::ignore_unused(alpha);
66 
67  P = m_PExt + beta * (sqrt(A) - sqrt(A0)) -
68  gamma * dAUdx / sqrt(A); // Viscoelasticity
69 }
70 
71 void BetaPressureArea::v_GetC(NekDouble &c, const NekDouble &beta,
72  const NekDouble &A, const NekDouble &A0,
73  const NekDouble &alpha)
74 {
75  boost::ignore_unused(A0, alpha);
76 
77  c = sqrt(beta / (2 * m_rho)) * sqrt(sqrt(A)); // Elastic
78 }
79 
80 void BetaPressureArea::v_GetW1(NekDouble &W1, const NekDouble &u,
81  const NekDouble &beta, const NekDouble &A,
82  const NekDouble &A0, const NekDouble &alpha)
83 {
84  boost::ignore_unused(alpha);
85 
86  NekDouble I = 0.0;
87  GetCharIntegral(I, beta, A, A0);
88 
89  W1 = u + I; // Elastic and assumes u0 = 0
90 }
91 
92 void BetaPressureArea::v_GetW2(NekDouble &W2, const NekDouble &u,
93  const NekDouble &beta, const NekDouble &A,
94  const NekDouble &A0, const NekDouble &alpha)
95 {
96  boost::ignore_unused(alpha);
97 
98  NekDouble I = 0.0;
99  GetCharIntegral(I, beta, A, A0);
100 
101  W2 = u - I; // Elastic and assumes u0 = 0
102 }
103 
104 void BetaPressureArea::v_GetAFromChars(NekDouble &A, const NekDouble &W1,
105  const NekDouble &W2,
106  const NekDouble &beta,
107  const NekDouble &A0,
108  const NekDouble &alpha)
109 {
110  boost::ignore_unused(alpha);
111 
112  A = pow((W1 - W2) * sqrt(2 * m_rho / beta) / 8 + sqrt(sqrt(A0)), 4);
113 }
114 
115 void BetaPressureArea::v_GetUFromChars(NekDouble &u, const NekDouble &W1,
116  const NekDouble &W2)
117 {
118  u = (W1 + W2) / 2; // Necessarily the case for all tube laws
119 }
120 
121 void BetaPressureArea::v_GetCharIntegral(NekDouble &I, const NekDouble &beta,
122  const NekDouble &A,
123  const NekDouble &A0,
124  const NekDouble &alpha)
125 {
126  boost::ignore_unused(alpha);
127 
128  NekDouble c = 0.0;
129  NekDouble c0 = 0.0;
130 
131  GetC(c, beta, A, A0);
132  GetC(c0, beta, A0, A0);
133 
134  I = 4 * (c - c0);
135 }
136 
137 void BetaPressureArea::v_GetJacobianInverse(NekMatrix<NekDouble> &invJ,
138  const Array<OneD, NekDouble> &Au,
139  const Array<OneD, NekDouble> &uu,
140  const Array<OneD, NekDouble> &beta,
141  const Array<OneD, NekDouble> &A0,
142  const Array<OneD, NekDouble> &alpha,
143  const std::string &type)
144 {
145  /*
146  In the interest of speed, the inverse of the Jacobians for bifurcations,
147  merges and junctions for the beta law have been calculated analytically.
148  This can be done for other laws too, or the general formulation can be used
149  instead.
150  */
151 
152  NekDouble k = 0.0;
153 
154  if (type == "Bifurcation")
155  {
156  NekMatrix<NekDouble> J(6, 6);
157  Array<OneD, NekDouble> c(3);
158  Array<OneD, NekDouble> K(3);
159 
160  for (int i = 0; i < 3; ++i)
161  {
162  GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
163  }
164 
165  k = c[0] * Au[1] * c[2] + Au[0] * c[2] * c[1] + Au[2] * c[0] * c[1];
166  K[0] = (c[0] - uu[0]) * k;
167  K[1] = (c[1] + uu[1]) * k;
168  K[2] = (c[2] + uu[2]) * k;
169 
170  invJ.SetValue(0, 0,
171  (-c[1] * uu[0] * c[2] * Au[0] +
172  Au[2] * c[1] * c[0] * c[0] +
173  Au[1] * c[0] * c[0] * c[2]) /
174  K[0]);
175  invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[0]);
176  invJ.SetValue(0, 2, Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[0]);
177  invJ.SetValue(0, 3, c[0] * c[1] * c[2] / K[0]);
178  invJ.SetValue(0, 4, -0.5 * c[0] * Au[1] * c[2] / K[0]);
179  invJ.SetValue(0, 5, -0.5 * Au[2] * c[0] * c[1] / K[0]);
180 
181  invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[1]);
182  invJ.SetValue(1, 1,
183  (c[0] * uu[1] * c[2] * Au[1] +
184  Au[2] * c[0] * c[1] * c[1] +
185  c[2] * c[1] * c[1] * Au[0]) /
186  K[1]);
187  invJ.SetValue(1, 2, -Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[1]);
188  invJ.SetValue(1, 3, -c[0] * c[1] * c[2] / K[1]);
189  invJ.SetValue(1, 4, -0.5 * (c[0] * Au[2] + Au[0] * c[2]) * c[1] / K[1]);
190  invJ.SetValue(1, 5, 0.5 * Au[2] * c[0] * c[1] / K[1]);
191 
192  invJ.SetValue(2, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[2]);
193  invJ.SetValue(2, 1, -Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[2]);
194  invJ.SetValue(2, 2,
195  (c[0] * c[1] * uu[2] * Au[2] +
196  c[0] * Au[1] * c[2] * c[2] +
197  c[1] * c[2] * c[2] * Au[0]) /
198  K[2]);
199  invJ.SetValue(2, 3, -c[0] * c[1] * c[2] / K[2]);
200  invJ.SetValue(2, 4, 0.5 * c[0] * Au[1] * c[2] / K[2]);
201  invJ.SetValue(2, 5, -0.5 * (Au[1] * c[0] + c[1] * Au[0]) * c[2] / K[2]);
202 
203  invJ.SetValue(3, 0,
204  Au[0] *
205  (Au[0] * c[2] * c[1] - uu[0] * c[2] * Au[1] -
206  uu[0] * c[1] * Au[2]) /
207  K[0]);
208  invJ.SetValue(3, 1, -Au[0] * Au[1] * (c[1] - uu[1]) * c[2] / K[0]);
209  invJ.SetValue(3, 2, -Au[0] * Au[2] * (c[2] - uu[2]) * c[1] / K[0]);
210  invJ.SetValue(3, 3, -Au[0] * c[2] * c[1] / K[0]);
211  invJ.SetValue(3, 4, 0.5 * Au[0] * Au[1] * c[2] / K[0]);
212  invJ.SetValue(3, 5, 0.5 * Au[0] * c[1] * Au[2] / K[0]);
213 
214  invJ.SetValue(4, 0, Au[0] * Au[1] * (c[0] + uu[0]) * c[2] / K[1]);
215  invJ.SetValue(4, 1,
216  -Au[1] *
217  (c[0] * Au[1] * c[2] + c[0] * uu[1] * Au[2] +
218  c[2] * uu[1] * Au[0]) /
219  K[1]);
220  invJ.SetValue(4, 2, -Au[2] * Au[1] * (c[2] - uu[2]) * c[0] / K[1]);
221  invJ.SetValue(4, 3, -c[0] * Au[1] * c[2] / K[1]);
222  invJ.SetValue(4, 4,
223  -0.5 * Au[1] * (c[0] * Au[2] + Au[0] * c[2]) / K[1]);
224  invJ.SetValue(4, 5, 0.5 * Au[2] * Au[1] * c[0] / K[1]);
225 
226  invJ.SetValue(5, 0, Au[0] * Au[2] * (c[0] + uu[0]) * c[1] / K[2]);
227  invJ.SetValue(5, 1, -Au[2] * Au[1] * (c[1] - uu[1]) * c[0] / K[2]);
228  invJ.SetValue(5, 2,
229  -Au[2] *
230  (Au[2] * c[0] * c[1] + c[0] * uu[2] * Au[1] +
231  c[1] * uu[2] * Au[0]) /
232  K[2]);
233  invJ.SetValue(5, 3, -Au[2] * c[0] * c[1] / K[2]);
234  invJ.SetValue(5, 4, 0.5 * Au[2] * Au[1] * c[0] / K[2]);
235  invJ.SetValue(5, 5,
236  -0.5 * Au[2] * (Au[1] * c[0] + c[1] * Au[0]) / K[2]);
237  }
238  else if (type == "Merge")
239  {
240  NekMatrix<NekDouble> J(6, 6);
241  Array<OneD, NekDouble> c(3);
242  Array<OneD, NekDouble> K(3);
243 
244  for (int i = 0; i < 3; ++i)
245  {
246  GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
247  }
248 
249  k = c[0] * Au[1] * c[2] + Au[0] * c[2] * c[1] + Au[2] * c[0] * c[1];
250  K[0] = (c[0] - uu[0]) * k;
251  K[1] = (c[1] + uu[1]) * k;
252  K[2] = (c[2] + uu[2]) * k;
253 
254  invJ.SetValue(0, 0,
255  (-c[1] * uu[0] * c[2] * Au[0] +
256  Au[2] * c[1] * c[0] * c[0] +
257  Au[1] * c[0] * c[0] * c[2]) /
258  K[0]);
259  invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] * c[2] / K[0]);
260  invJ.SetValue(0, 2, Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[0]);
261  invJ.SetValue(0, 3, c[0] * c[1] * c[2] / K[0]);
262  invJ.SetValue(0, 4, -0.5 * c[0] * Au[1] * c[2] / K[0]);
263  invJ.SetValue(0, 5, -0.5 * Au[2] * c[0] * c[1] / K[0]);
264 
265  invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] * c[2] / K[1]);
266  invJ.SetValue(1, 1,
267  (c[0] * uu[1] * c[2] * Au[1] +
268  Au[2] * c[0] * c[1] * c[1] +
269  c[2] * c[1] * c[1] * Au[0]) /
270  K[1]);
271  invJ.SetValue(1, 2, -Au[2] * (c[2] - uu[2]) * c[0] * c[1] / K[1]);
272  invJ.SetValue(1, 3, -c[0] * c[1] * c[2] / K[1]);
273  invJ.SetValue(1, 4, -0.5 * (c[0] * Au[2] + Au[0] * c[2]) * c[1] / K[1]);
274  invJ.SetValue(1, 5, 0.5 * Au[2] * c[0] * c[1] / K[1]);
275 
276  invJ.SetValue(2, 0, Au[0] * (c[0] - uu[0]) * c[1] * c[2] / K[2]);
277  invJ.SetValue(2, 1, -Au[1] * (c[1] + uu[1]) * c[0] * c[2] / K[2]);
278  invJ.SetValue(2, 2,
279  -(c[0] * uu[2] * c[1] * Au[2] -
280  Au[1] * c[0] * c[2] * c[2] -
281  c[1] * c[2] * c[2] * Au[0]) /
282  K[2]);
283  invJ.SetValue(2, 3, -c[0] * c[1] * c[2] / K[2]);
284  invJ.SetValue(2, 4, -0.5 * Au[1] * c[0] * c[2] / K[2]);
285  invJ.SetValue(2, 5, 0.5 * (Au[1] * c[0] + Au[0] * c[1]) * c[2] / K[2]);
286 
287  invJ.SetValue(3, 0,
288  -Au[0] *
289  (Au[0] * c[2] * c[1] + uu[0] * c[2] * Au[1] +
290  uu[0] * c[1] * Au[2]) /
291  K[0]);
292  invJ.SetValue(3, 1, Au[0] * Au[1] * (c[1] + uu[1]) * c[2] / K[0]);
293 
294  invJ.SetValue(3, 2, -Au[0] * Au[2] * (c[2] - uu[2]) * c[1] / K[0]);
295  invJ.SetValue(3, 3, -Au[0] * c[2] * c[1] / K[0]);
296  invJ.SetValue(3, 4, 0.5 * Au[0] * Au[1] * c[2] / K[0]);
297  invJ.SetValue(3, 5, 0.5 * Au[0] * c[1] * Au[2] / K[0]);
298 
299  invJ.SetValue(4, 0, Au[0] * Au[1] * (c[0] + uu[0]) * c[2] / K[1]);
300  invJ.SetValue(4, 1,
301  -Au[1] *
302  (c[0] * Au[1] * c[2] + c[0] * uu[1] * Au[2] +
303  c[2] * uu[1] * Au[0]) /
304  K[1]);
305  invJ.SetValue(4, 2, -Au[2] * Au[1] * (c[2] - uu[2]) * c[0] / K[1]);
306  invJ.SetValue(4, 3, -c[0] * Au[1] * c[2] / K[1]);
307  invJ.SetValue(4, 4,
308  -0.5 * Au[1] * (c[0] * Au[2] + Au[0] * c[2]) / K[1]);
309  invJ.SetValue(4, 5, 0.5 * Au[2] * Au[1] * c[0] / K[1]);
310 
311  invJ.SetValue(5, 0, Au[0] * Au[2] * (c[0] + uu[0]) * c[1] / K[2]);
312  invJ.SetValue(5, 1, -Au[2] * Au[1] * (c[1] - uu[1]) * c[0] / K[2]);
313  invJ.SetValue(5, 2,
314  -Au[2] *
315  (Au[2] * c[0] * c[1] + c[0] * uu[2] * Au[1] +
316  c[1] * uu[2] * Au[0]) /
317  K[2]);
318  invJ.SetValue(5, 3, -Au[2] * c[0] * c[1] / K[2]);
319  invJ.SetValue(5, 4, 0.5 * Au[2] * Au[1] * c[0] / K[2]);
320  invJ.SetValue(5, 5,
321  -0.5 * Au[2] * (Au[1] * c[0] + c[1] * Au[0]) / K[2]);
322  }
323  else if (type == "Interface")
324  {
325  NekMatrix<NekDouble> J(4, 4);
326  Array<OneD, NekDouble> c(2);
327  Array<OneD, NekDouble> K(2);
328 
329  for (int i = 0; i < 2; ++i)
330  {
331  GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
332  }
333 
334  k = (c[0] * Au[1] + Au[0] * c[1]);
335  K[0] = (c[0] + uu[0]) * k;
336  K[1] = (c[1] + uu[1]) * k;
337 
338  invJ.SetValue(0, 0,
339  (Au[1] * c[0] * c[0] - c[1] * uu[0] * Au[0]) / K[0]);
340  invJ.SetValue(0, 1, Au[1] * (c[1] - uu[1]) * c[0] / K[0]);
341  invJ.SetValue(0, 2, c[0] * c[1] / K[0]);
342  invJ.SetValue(0, 3, -0.5 * c[0] * Au[1] / K[0]);
343 
344  invJ.SetValue(1, 0, Au[0] * (c[0] + uu[0]) * c[1] / K[1]);
345  invJ.SetValue(1, 1,
346  (c[0] * uu[1] * Au[1] + c[1] * c[1] * Au[0]) / K[1]);
347  invJ.SetValue(1, 2, -c[0] * c[1] / K[1]);
348  invJ.SetValue(1, 3, -0.5 * Au[0] * c[1] / K[1]);
349 
350  invJ.SetValue(2, 0, Au[0] * (Au[0] * c[1] - uu[0] * Au[1]) / K[0]);
351  invJ.SetValue(2, 1, -Au[0] * Au[1] * (c[1] - uu[1]) / K[0]);
352  invJ.SetValue(2, 2, -Au[0] * c[1] / K[0]);
353  invJ.SetValue(2, 3, 0.5 * Au[1] * Au[0] / K[0]);
354 
355  invJ.SetValue(3, 0, Au[0] * Au[1] * (c[0] + uu[0]) / K[1]);
356  invJ.SetValue(3, 1, -Au[1] * (c[0] * Au[1] + uu[1] * Au[0]) / K[1]);
357  invJ.SetValue(3, 2, -c[0] * Au[1] / K[1]);
358  invJ.SetValue(3, 3, -0.5 * Au[1] * Au[0] / K[1]);
359  }
360 }
361 
362 } // namespace Nektar
Nektar::BetaPressureArea::v_GetPressure
virtual void v_GetPressure(NekDouble &P, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &dAUdx, const NekDouble &gamma=0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:59
Nektar::BetaPressureArea::v_GetCharIntegral
virtual void v_GetCharIntegral(NekDouble &I, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:121
Nektar::BetaPressureArea::v_GetW2
virtual void v_GetW2(NekDouble &W2, const NekDouble &u, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:92
Nektar::BetaPressureArea::v_GetUFromChars
virtual void v_GetUFromChars(NekDouble &u, const NekDouble &W1, const NekDouble &W2) override
Definition: BetaPressureArea.cpp:115
Nektar::BetaPressureArea::v_GetC
virtual void v_GetC(NekDouble &c, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:71
Nektar::BetaPressureArea::v_GetJacobianInverse
virtual void v_GetJacobianInverse(NekMatrix< NekDouble > &invJ, const Array< OneD, NekDouble > &Au, const Array< OneD, NekDouble > &uu, const Array< OneD, NekDouble > &beta, const Array< OneD, NekDouble > &A0, const Array< OneD, NekDouble > &alpha, const std::string &type) override
Definition: BetaPressureArea.cpp:137
Nektar::BetaPressureArea::v_GetW1
virtual void v_GetW1(NekDouble &W1, const NekDouble &u, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:80
Nektar::BetaPressureArea::v_GetAFromChars
virtual void v_GetAFromChars(NekDouble &A, const NekDouble &W1, const NekDouble &W2, const NekDouble &beta, const NekDouble &A0, const NekDouble &alpha=0.5) override
Definition: BetaPressureArea.cpp:104
Nektar::LibUtilities::NekFactory::RegisterCreatorFunction
tKey RegisterCreatorFunction(tKey idKey, CreatorFunction classCreator, std::string pDesc="")
Register a class with the factory.
Definition: NekFactory.hpp:198
Nektar::PulseWavePressureArea::GetCharIntegral
void GetCharIntegral(NekDouble &I, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5)
Definition: PulseWavePressureArea.h:197
Nektar::PulseWavePressureArea::GetC
void GetC(NekDouble &c, const NekDouble &beta, const NekDouble &A, const NekDouble &A0, const NekDouble &alpha=0.5)
Definition: PulseWavePressureArea.h:158
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std::shared_ptr< SessionReader > SessionReaderSharedPtr
Definition: SessionReader.h:115
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@ beta
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Definition: PointsType.h:61
Nektar
The above copyright notice and this permission notice shall be included.
Definition: CoupledSolver.h:2
Nektar::GetPressureAreaFactory
PressureAreaFactory & GetPressureAreaFactory()
Definition: PulseWavePressureArea.cpp:54
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