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DtNmap2Dvisc.hh
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1
9#ifndef dtn_map2d_visc_hh
10#define dtn_map2d_visc_hh
11
12#include "basics/exceptions.hh"
13#include "toolbox/sequence.hh"
14#include "space/integral.hh"
15#include "formula/elementFormulaContainer.hh"
16#include "formula/formulas2D.hh"
17#include "formula/bessel.hh"
18#include "formula/frmE_product.hh"
19#include "function/vector.hh"
20#include "operator/sparseMatrix.hh"
21#include "hp1D/linearForm.hh"
22
23namespace concepts {
24
25
26 // ***************************************************** lambda_j_fast *
27
30 Cmplx lambda_j_fast(const Real L,
31 const Real omega,
32 const Real c,
33 const Real rho0,
34 const Real nu,
35 const uint j)
36 {
37 Cmplx lambda;
38 Real a,b;
39 a = (2.0*j*M_PI/L)*(2.0*j*M_PI/L);
40 b = -omega*rho0/nu;
41#if __cplusplus >= 201103L
42 lambda.real(-1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)+a));
43 lambda.imag(1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)-a));
44#else
45 lambda.real() = -1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)+a);
46 lambda.imag() = 1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)-a);
47#endif
48 return lambda;
49 }
50
51 // ***************************************************** lambda_j_slow *
52
55 Cmplx lambda_j_slow(const Real L,
56 const Real omega,
57 const Real c,
58 const Real rho0,
59 const Real nu,
60 const uint j)
61 {
62 Cmplx lambda;
63 Real a,b;
64 a = (2.0*j*M_PI/L)*(2.0*j*M_PI/L)
65 - (c*c*omega*omega)/(c*c*c*c+omega*omega*nu*nu/(rho0*rho0));
66 b = -(nu/rho0*omega*omega*omega)/(c*c*c*c+omega*omega*nu*nu/(rho0*rho0));
67#if __cplusplus >= 201103L
68 lambda.real(-1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)+a));
69 lambda.imag(1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)-a));
70#else
71 lambda.real() = -1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)+a);
72 lambda.imag() = 1.0/sqrt(2.0)*sqrt(sqrt(a*a+b*b)-a);
73#endif
74 return lambda;
75 }
76
77 // ***************************************************** g_fast *
80 Cmplx g_fast(const Real L,
81 const Real omega,
82 const Real c,
83 const Real rho0,
84 const Real nu,
85 const uint j)
86 {
87 Cmplx g;
88#if __cplusplus >= 201103L
89 g.real(-c*c*rho0*(2.0*j*M_PI/L)*(2.0*j*M_PI/L));
90 g.imag(0.);
91#else
92 g.real() = -c*c*rho0*(2.0*j*M_PI/L)*(2.0*j*M_PI/L);
93 g.imag() = 0.;
94#endif
95 return g;
96 }
97
98 // ***************************************************** g_slow *
101 Cmplx g_slow(const Real L,
102 const Real omega,
103 const Real c,
104 const Real rho0,
105 const Real nu,
106 const uint j)
107 {
108 Cmplx g;
109#if __cplusplus >= 201103L
110 g.real(omega*omega*rho0-c*c*rho0*(2.0*j*M_PI/L)*(2.0*j*M_PI/L)
111 - (omega*omega*omega*omega*nu*nu/rho0)/(c*c*c*c+nu*nu*omega*omega/(rho0*rho0)));
112 g.imag(omega*omega*omega*nu*c*c/(c*c*c*c+nu*nu*omega*omega/(rho0*rho0)));
113#else
114 g.real() = omega*omega*rho0-c*c*rho0*(2.0*j*M_PI/L)*(2.0*j*M_PI/L)
115 - (omega*omega*omega*omega*nu*nu/rho0)/(c*c*c*c+nu*nu*omega*omega/(rho0*rho0));
116 g.imag() = omega*omega*omega*nu*c*c/(c*c*c*c+nu*nu*omega*omega/(rho0*rho0));
117#endif
118 return g;
119 }
120
121
122
123 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partDn(const Real L,
124 const Real omega,
125 const Real c,
126 const Real rho0,
127 const Real nu,
128 uint N=0)
129 {
130
131 Sequence<int> nSeq = makeRangeSequence(N+1);
132 Sequence<Cmplx> DtNCoeff(N+1);
133 DtNCoeff[0] = lambda_j_slow(L,omega,c,rho0,nu,0);
134 for(uint j=1;j <= N; j++)
135 {
136 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j);
137 Cmplx ljs = lambda_j_slow(L,omega,c,rho0,nu,j);
138 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j);
139 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j);
140 DtNCoeff[j] = ljf*ljs*(gjf-gjs)
141 /(gjf*ljs-gjs*ljf);
142 }
143 return DtNCoeff;
144 }
145
146 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partDt(const Real L,
147 const Real omega,
148 const Real c,
149 const Real rho0,
150 const Real nu,
151 uint N=1)
152 {
153
154 Sequence<int> nSeq = makeRangeSequence(N);
155 Sequence<Cmplx> DtNCoeff(N);
156 for(uint j=0;j < N; j++)
157 {
158 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j+1);
159 Cmplx ljs = sqrt(nu)*lambda_j_slow(L,omega,c,rho0,nu,j+1);
160 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j+1);
161 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j+1);
162 DtNCoeff[j] = 2.0 * (j+1) * M_PI / L
163 - 1.0 / (c*c*rho0 * 2.0 * (j+1) * M_PI / L)
164 * ((ljf-ljs)*gjf*gjs) / (gjf*ljs-gjs*ljf);
165 }
166 return DtNCoeff;
167 }
168
169 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partDttilde(const Real L,
170 const Real omega,
171 const Real c,
172 const Real rho0,
173 const Real nu,
174 uint N=1)
175 {
176
177 Sequence<int> nSeq = makeRangeSequence(N);
178 Sequence<Cmplx> DtNCoeff(N);
179 for(uint j=0;j < N; j++)
180 {
181 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j+1);
182 Cmplx ljs = sqrt(nu)*lambda_j_slow(L,omega,c,rho0,nu,j+1);
183 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j+1);
184 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j+1);
185 DtNCoeff[j] = - 1.0 / (c*c*rho0 *2.0 * (j+1) * M_PI / L)
186 * ((ljf-ljs)*gjf*gjs) / (gjf*ljs-gjs*ljf);
187 }
188 return DtNCoeff;
189 }
190
191 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partRn(const Real L,
192 const Real omega,
193 const Real c,
194 const Real rho0,
195 const Real nu,
196 uint N=1)
197 {
198
199 Sequence<int> nSeq = makeRangeSequence(N);
200 Sequence<Cmplx> DtNCoeff(N);
201 for(uint j=0;j < N; j++)
202 {
203 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j+1);
204 Cmplx ljs = lambda_j_slow(L,omega,c,rho0,nu,j+1);
205 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j+1);
206 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j+1);
207 DtNCoeff[j] = nu * 2.0 * (j+1) * M_PI / L
208 + c*c*rho0 * 2.0 * (j+1) * M_PI / L
209 * nu *((ljf-ljs)*ljs*ljf) / (gjf*ljs-gjs*ljf);
210 }
211 return DtNCoeff;
212 }
213
214 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partRntilde(const Real L,
215 const Real omega,
216 const Real c,
217 const Real rho0,
218 const Real nu,
219 uint N=1)
220 {
221
222 Sequence<int> nSeq = makeRangeSequence(N);
223 Sequence<Cmplx> DtNCoeff(N);
224 for(uint j=0;j < N; j++)
225 {
226 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j+1);
227 Cmplx ljs = lambda_j_slow(L,omega,c,rho0,nu,j+1);
228 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j+1);
229 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j+1);
230 DtNCoeff[j] = c*c*rho0 * 2.0 * (j+1) * M_PI / L
231 * nu *((ljf-ljs)*ljs*ljf) / (gjf*ljs-gjs*ljf);
232 }
233 return DtNCoeff;
234 }
235
236 Sequence<Cmplx> getNSDtNCoeff_Straight2D_partRt(const Real L,
237 const Real omega,
238 const Real c,
239 const Real rho0,
240 const Real nu,
241 uint N=0)
242 {
243
244 Sequence<int> nSeq = makeRangeSequence(N+1);
245 Sequence<Cmplx> DtNCoeff(N+1);
246 DtNCoeff[0] = nu*lambda_j_fast(L,omega,c,rho0,nu,0);
247 for(uint j=1;j <= N; j++)
248 {
249 Cmplx ljf = lambda_j_fast(L,omega,c,rho0,nu,j);
250 Cmplx ljs = lambda_j_slow(L,omega,c,rho0,nu,j);
251 Cmplx gjf = g_fast(L,omega,c,rho0,nu,j);
252 Cmplx gjs = g_slow(L,omega,c,rho0,nu,j);
253 DtNCoeff[j] = nu*(gjf*ljs*ljs-gjs*ljf*ljf)
254 /(gjf*ljs-gjs*ljf);
255 }
256 return DtNCoeff;
257 }
258
259} // namespace concepts
260
261#endif // dtn_map2d_visc_hh
frmE_product.hh
concepts::g_slow
Cmplx g_slow(const Real L, const Real omega, const Real c, const Real rho0, const Real nu, const uint j)
Definition DtNmap2Dvisc.hh:101
concepts::g_fast
Cmplx g_fast(const Real L, const Real omega, const Real c, const Real rho0, const Real nu, const uint j)
Definition DtNmap2Dvisc.hh:80
concepts::Real
double Real
Definition typedefs.hh:39
concepts::makeRangeSequence
Sequence< int > makeRangeSequence(uint n)
Returns the sequence 0,1,...,n-1.
concepts::makeSet
Set< F > makeSet(uint n, const F &first,...)
Definition set.hh:320
concepts::lambda_j_slow
Cmplx lambda_j_slow(const Real L, const Real omega, const Real c, const Real rho0, const Real nu, const uint j)
Definition DtNmap2Dvisc.hh:55
concepts::Cmplx
std::complex< Real > Cmplx
Type for a complex number. It also depends on the setting of Real.
Definition typedefs.hh:42
concepts::lambda_j_fast
Cmplx lambda_j_fast(const Real L, const Real omega, const Real c, const Real rho0, const Real nu, const uint j)
Definition DtNmap2Dvisc.hh:30
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