Nektar++
BetaPressureArea.cpp
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2//
3// File: BetaPressureArea.cpp
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9// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
10// Department of Aeronautics, Imperial College London (UK), and Scientific
11// Computing and Imaging Institute, University of Utah (USA).
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31//
32// Description: BetaPressureArea class
33//
34///////////////////////////////////////////////////////////////////////////////
35
36#include <PulseWaveSolver/EquationSystems/BetaPressureArea.h>
37
38using namespace std;
39
40namespace Nektar
41{
42
43std::string BetaPressureArea::className =
44 GetPressureAreaFactory().RegisterCreatorFunction(
45 "Beta", BetaPressureArea::create,
46 "Beta law pressure area relationship for the arterial system");
47
48BetaPressureArea::BetaPressureArea(
49 Array<OneD, MultiRegions::ExpListSharedPtr> pVessel,
50 const LibUtilities::SessionReaderSharedPtr pSession)
51 : PulseWavePressureArea(pVessel, pSession)
52{
53}
54
55BetaPressureArea::~BetaPressureArea()
56{
57}
58
59void 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
71void 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
80void 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
92void 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
104void 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
115void 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
121void 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
137void 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::BetaPressureArea
BetaPressureArea(Array< OneD, MultiRegions::ExpListSharedPtr > pVessel, const LibUtilities::SessionReaderSharedPtr pSession)
Definition: BetaPressureArea.cpp:48
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::create
static PulseWavePressureAreaSharedPtr create(Array< OneD, MultiRegions::ExpListSharedPtr > &pVessel, const LibUtilities::SessionReaderSharedPtr &pSession)
Definition: BetaPressureArea.h:53
Nektar::BetaPressureArea::className
static std::string className
Definition: BetaPressureArea.h:61
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
Nektar::LibUtilities::SessionReaderSharedPtr
std::shared_ptr< SessionReader > SessionReaderSharedPtr
Definition: SessionReader.h:115
Nektar::LibUtilities::beta
@ beta
Gauss Radau pinned at x=-1,.
Definition: PointsType.h:61
Nektar::LibUtilities::P
@ P
Monomial polynomials .
Definition: BasisType.h:64
Nektar
The above copyright notice and this permission notice shall be included.
Definition: CoupledSolver.h:2
Nektar::GetPressureAreaFactory
PressureAreaFactory & GetPressureAreaFactory()
Definition: PulseWavePressureArea.cpp:54
Nektar::NekDouble
double NekDouble
Definition: NektarUnivTypeDefs.hpp:43
tinysimd::sqrt
scalarT< T > sqrt(scalarT< T > in)
Definition: scalar.hpp:294
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