src/foam/primitives/Tensor2D/Tensor2DI.H

   1 /*---------------------------------------------------------------------------*\
   2   =========                 |
   3   \\      /  F ield         | foam-extend: Open Source CFD
   4    \\    /   O peration     |
   5     \\  /    A nd           | For copyright notice see file Copyright
   6      \\/     M anipulation  |
   7 -------------------------------------------------------------------------------
   8 License
   9     This file is part of foam-extend.
  10
  11     foam-extend is free software: you can redistribute it and/or modify it
  12     under the terms of the GNU General Public License as published by the
  13     Free Software Foundation, either version 3 of the License, or (at your
  14     option) any later version.
  15
  16     foam-extend is distributed in the hope that it will be useful, but
  17     WITHOUT ANY WARRANTY; without even the implied warranty of
  18     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  19     General Public License for more details.
  20
  21     You should have received a copy of the GNU General Public License
  22     along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.
  23
  24 \*---------------------------------------------------------------------------*/
  25
  26 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
  27
  28 namespace Foam
  29 {
  30
  31 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
  32
  33 template <class Cmpt>
  34 inline Tensor2D<Cmpt>::Tensor2D()
  35 {}
  36
  37
  38 template <class Cmpt>
  39 inline Tensor2D<Cmpt>::Tensor2D(const VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>& vs)
  40 :
  41     VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(vs)
  42 {}
  43
  44
  45 template <class Cmpt>
  46 inline Tensor2D<Cmpt>::Tensor2D(const SphericalTensor2D<Cmpt>& st)
  47 {
  48     this->v_[XX] = st.ii(); this->v_[XY] = 0;
  49     this->v_[YX] = 0; this->v_[YY] = st.ii();
  50 }
  51
  52
  53 template <class Cmpt>
  54 inline Tensor2D<Cmpt>::Tensor2D
  55 (
  56     const Vector2D<Cmpt>& x,
  57     const Vector2D<Cmpt>& y
  58 )
  59 {
  60     this->v_[XX] = x.x(); this->v_[XY] = x.y();
  61     this->v_[YX] = y.x(); this->v_[YY] = y.y();
  62 }
  63
  64
  65 template <class Cmpt>
  66 inline Tensor2D<Cmpt>::Tensor2D
  67 (
  68     const Cmpt txx, const Cmpt txy,
  69     const Cmpt tyx, const Cmpt tyy
  70 )
  71 {
  72     this->v_[XX] = txx; this->v_[XY] = txy;
  73     this->v_[YX] = tyx; this->v_[YY] = tyy;
  74 }
  75
  76
  77 template <class Cmpt>
  78 inline Tensor2D<Cmpt>::Tensor2D(Istream& is)
  79 :
  80     VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(is)
  81 {}
  82
  83
  84 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
  85
  86 template <class Cmpt>
  87 inline Vector2D<Cmpt> Tensor2D<Cmpt>::x() const
  88 {
  89     return Vector2D<Cmpt>(this->v_[XX], this->v_[XY]);
  90 }
  91
  92 template <class Cmpt>
  93 inline Vector2D<Cmpt> Tensor2D<Cmpt>::y() const
  94 {
  95     return Vector2D<Cmpt>(this->v_[YX], this->v_[YY]);
  96 }
  97
  98
  99 template <class Cmpt>
 100 inline const Cmpt& Tensor2D<Cmpt>::xx() const
 101 {
 102     return this->v_[XX];
 103 }
 104
 105
 106 template <class Cmpt>
 107 inline const Cmpt& Tensor2D<Cmpt>::xy() const
 108 {
 109     return this->v_[XY];
 110 }
 111
 112
 113 template <class Cmpt>
 114 inline const Cmpt& Tensor2D<Cmpt>::yx() const
 115 {
 116     return this->v_[YX];
 117 }
 118
 119
 120 template <class Cmpt>
 121 inline const Cmpt& Tensor2D<Cmpt>::yy() const
 122 {
 123     return this->v_[YY];
 124 }
 125
 126
 127 template <class Cmpt>
 128 inline Cmpt& Tensor2D<Cmpt>::xx()
 129 {
 130     return this->v_[XX];
 131 }
 132
 133
 134 template <class Cmpt>
 135 inline Cmpt& Tensor2D<Cmpt>::xy()
 136 {
 137     return this->v_[XY];
 138 }
 139
 140
 141 template <class Cmpt>
 142 inline Cmpt& Tensor2D<Cmpt>::yx()
 143 {
 144     return this->v_[YX];
 145 }
 146
 147
 148 template <class Cmpt>
 149 inline Cmpt& Tensor2D<Cmpt>::yy()
 150 {
 151     return this->v_[YY];
 152 }
 153
 154
 155 template <class Cmpt>
 156 inline const Cmpt& Tensor2D<Cmpt>::operator()
 157 (
 158     const direction i,
 159     const direction j
 160 ) const
 161 {
 162     return this->operator[](i*Tensor2D<Cmpt>::dim + j);
 163 }
 164
 165
 166 template <class Cmpt>
 167 inline Cmpt& Tensor2D<Cmpt>::operator()
 168 (
 169     const direction i,
 170     const direction j
 171 )
 172 {
 173     return this->operator[](i*Tensor2D<Cmpt>::dim + j);
 174 }
 175
 176
 177 template <class Cmpt>
 178 inline Tensor2D<Cmpt> Tensor2D<Cmpt>::T() const
 179 {
 180     return Tensor2D<Cmpt>
 181     (
 182         xx(), yx(),
 183         xy(), yy()
 184     );
 185 }
 186
 187
 188 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 189
 190 template <class Cmpt>
 191 inline void Tensor2D<Cmpt>::operator=(const SphericalTensor2D<Cmpt>& st)
 192 {
 193     this->v_[XX] = st.ii(); this->v_[XY] = 0;
 194     this->v_[YX] = 0; this->v_[YY] = st.ii();
 195 }
 196
 197
 198
 199 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 200
 201 //- Inner-product between two tensors
 202 template <class Cmpt>
 203 inline typename innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt> >::type
 204 operator&(const Tensor2D<Cmpt>& t1, const Tensor2D<Cmpt>& t2)
 205 {
 206     return Tensor2D<Cmpt>
 207     (
 208         t1.xx()*t2.xx() + t1.xy()*t2.yx(),
 209         t1.xx()*t2.xy() + t1.xy()*t2.yy(),
 210
 211         t1.yx()*t2.xx() + t1.yy()*t2.yx(),
 212         t1.yx()*t2.xy() + t1.yy()*t2.yy()
 213     );
 214 }
 215
 216 //- Inner-product between a tensor and a vector
 217 template <class Cmpt>
 218 inline typename innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt> >::type
 219 operator&(const Tensor2D<Cmpt>& t, const Vector2D<Cmpt>& v)
 220 {
 221     return Vector2D<Cmpt>
 222     (
 223         t.xx()*v.x() + t.xy()*v.y(),
 224         t.yx()*v.x() + t.yy()*v.y()
 225     );
 226 }
 227
 228 //- Inner-product between a vector and a tensor
 229 template <class Cmpt>
 230 inline typename innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt> >::type
 231 operator&(const Vector2D<Cmpt>& v, const Tensor2D<Cmpt>& t)
 232 {
 233     return Vector2D<Cmpt>
 234     (
 235         v.x()*t.xx() + v.y()*t.yx(),
 236         v.x()*t.xy() + v.y()*t.yy()
 237     );
 238 }
 239
 240 //- Outer-product between two vectors
 241 template <class Cmpt>
 242 inline typename outerProduct<Vector2D<Cmpt>, Vector2D<Cmpt> >::type
 243 operator*(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
 244 {
 245     return Tensor2D<Cmpt>
 246     (
 247         v1.x()*v2.x(), v1.x()*v2.y(),
 248         v1.y()*v2.x(), v1.y()*v2.y()
 249     );
 250 }
 251
 252
 253 //- Return the trace of a tensor
 254 template <class Cmpt>
 255 inline Cmpt tr(const Tensor2D<Cmpt>& t)
 256 {
 257     return t.xx() + t.yy();
 258 }
 259
 260
 261 //- Return the spherical part of a tensor
 262 template <class Cmpt>
 263 inline SphericalTensor2D<Cmpt> sph(const Tensor2D<Cmpt>& t)
 264 {
 265     return 0.5*tr(t);
 266 }
 267
 268
 269 //- Return the symmetric part of a tensor
 270 template <class Cmpt>
 271 inline Tensor2D<Cmpt> symm(const Tensor2D<Cmpt>& t)
 272 {
 273     return Tensor2D<Cmpt>
 274     (
 275         t.xx(), 0.5*(t.xy() + t.yx()),
 276         0.5*(t.yx() + t.xy()), t.yy()
 277     );
 278 }
 279
 280 //- Return the twice the symmetric part of a tensor
 281 template <class Cmpt>
 282 inline Tensor2D<Cmpt> twoSymm(const Tensor2D<Cmpt>& t)
 283 {
 284     return Tensor2D<Cmpt>
 285     (
 286         t.xx() + t.xx(), t.xy() + t.yx(),
 287         t.yx() + t.xy(), t.yy() + t.yy()
 288     );
 289 }
 290
 291 //- Return the skew-symmetric part of a tensor
 292 template <class Cmpt>
 293 inline Tensor2D<Cmpt> skew(const Tensor2D<Cmpt>& t)
 294 {
 295     return Tensor2D<Cmpt>
 296     (
 297         0.0, 0.5*(t.xy() - t.yx()),
 298         0.5*(t.yx() - t.xy()), 0.0
 299     );
 300 }
 301
 302
 303 //- Return the deviatoric part of a tensor
 304 template <class Cmpt>
 305 inline Tensor2D<Cmpt> dev(const Tensor2D<Cmpt>& t)
 306 {
 307     return t - SphericalTensor2D<Cmpt>::oneThirdI*tr(t);
 308 }
 309
 310
 311 //- Return the deviatoric part of a tensor
 312 template <class Cmpt>
 313 inline Tensor2D<Cmpt> dev2(const Tensor2D<Cmpt>& t)
 314 {
 315     return t - SphericalTensor2D<Cmpt>::twoThirdsI*tr(t);
 316 }
 317
 318
 319 //- Return the determinant of a tensor
 320 template <class Cmpt>
 321 inline Cmpt det(const Tensor2D<Cmpt>& t)
 322 {
 323     return(t.xx()*t.yy() - t.xy()*t.yx());
 324 }
 325
 326
 327 //- Return the cofactor tensor of a tensor
 328 template <class Cmpt>
 329 inline Tensor2D<Cmpt> cof(const Tensor2D<Cmpt>& t)
 330 {
 331     return Tensor2D<Cmpt>
 332     (
 333         t.yy(), -t.xy(),
 334        -t.yx(),  t.xx()
 335     );
 336 }
 337
 338
 339 //- Return the inverse of a tensor given the determinant
 340 template <class Cmpt>
 341 inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt dett)
 342 {
 343     return cof(t)/dett;
 344 }
 345
 346
 347 //- Return the inverse of a tensor
 348 template <class Cmpt>
 349 inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t)
 350 {
 351     return inv(t, det(t));
 352 }
 353
 354
 355 //- Return the 1st invariant of a tensor
 356 template <class Cmpt>
 357 inline Cmpt invariantI(const Tensor2D<Cmpt>& t)
 358 {
 359     return tr(t);
 360 }
 361
 362
 363 //- Return the 2nd invariant of a tensor
 364 template <class Cmpt>
 365 inline Cmpt invariantII(const Tensor2D<Cmpt>& t)
 366 {
 367     return
 368     (
 369         0.5*sqr(tr(t))
 370       - 0.5*
 371         (
 372            t.xx()*t.xx() + t.xy()*t.xy()
 373          + t.yx()*t.yx() + t.yy()*t.yy()
 374         )
 375     );
 376 }
 377
 378
 379 //- Return the 3rd invariant of a tensor
 380 template <class Cmpt>
 381 inline Cmpt invariantIII(const Tensor2D<Cmpt>& t)
 382 {
 383     return det(t);
 384 }
 385
 386
 387
 388
 389 template <class Cmpt>
 390 inline Tensor2D<Cmpt>
 391 operator+(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 392 {
 393     return Tensor2D<Cmpt>
 394     (
 395         st1.ii() + t2.xx(), t2.xy(),
 396         t2.yx(),            st1.ii() + t2.yy()
 397     );
 398 }
 399
 400
 401 template <class Cmpt>
 402 inline Tensor2D<Cmpt>
 403 operator+(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 404 {
 405     return Tensor2D<Cmpt>
 406     (
 407         t1.xx() + st2.ii(), t1.xy(),
 408         t1.yx(),            t1.yy() + st2.ii()
 409     );
 410 }
 411
 412
 413 template <class Cmpt>
 414 inline Tensor2D<Cmpt>
 415 operator-(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 416 {
 417     return Tensor2D<Cmpt>
 418     (
 419         st1.ii() - t2.xx(), -t2.xy(),
 420        -t2.yx(),             st1.ii() - t2.yy()
 421     );
 422 }
 423
 424
 425 template <class Cmpt>
 426 inline Tensor2D<Cmpt>
 427 operator-(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 428 {
 429     return Tensor2D<Cmpt>
 430     (
 431         t1.xx() - st2.ii(), t1.xy(),
 432         t1.yx(),            t1.yy() - st2.ii()
 433     );
 434 }
 435
 436
 437 //- Inner-product between a spherical tensor and a tensor
 438 template <class Cmpt>
 439 inline Tensor2D<Cmpt>
 440 operator&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 441 {
 442     return Tensor2D<Cmpt>
 443     (
 444         st1.ii()*t2.xx(),
 445         st1.ii()*t2.xy(),
 446                           st1.ii()*t2.yx(),
 447                           st1.ii()*t2.yy()
 448     );
 449 }
 450
 451
 452 //- Inner-product between a tensor and a spherical tensor
 453 template <class Cmpt>
 454 inline Tensor2D<Cmpt>
 455 operator&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 456 {
 457     return Tensor2D<Cmpt>
 458     (
 459         t1.xx()*st2.ii(),
 460                           t1.xy()*st2.ii(),
 461
 462         t1.yx()*st2.ii(),
 463                           t1.yy()*st2.ii()
 464     );
 465 }
 466
 467
 468 //- Double-dot-product between a spherical tensor and a tensor
 469 template <class Cmpt>
 470 inline Cmpt
 471 operator&&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 472 {
 473     return(st1.ii()*t2.xx() + st1.ii()*t2.yy());
 474 }
 475
 476
 477 //- Double-dot-product between a tensor and a spherical tensor
 478 template <class Cmpt>
 479 inline Cmpt
 480 operator&&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 481 {
 482     return(t1.xx()*st2.ii() + t1.yy()*st2.ii());
 483 }
 484
 485
 486 template<class Cmpt>
 487 class typeOfSum<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
 488 {
 489 public:
 490
 491     typedef Tensor2D<Cmpt> type;
 492 };
 493
 494 template<class Cmpt>
 495 class typeOfSum<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
 496 {
 497 public:
 498
 499     typedef Tensor2D<Cmpt> type;
 500 };
 501
 502
 503 template<class Cmpt>
 504 class innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt> >
 505 {
 506 public:
 507
 508     typedef Tensor2D<Cmpt> type;
 509 };
 510
 511 template<class Cmpt>
 512 class innerProduct<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
 513 {
 514 public:
 515
 516     typedef Tensor2D<Cmpt> type;
 517 };
 518
 519 template<class Cmpt>
 520 class innerProduct<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
 521 {
 522 public:
 523
 524     typedef Tensor2D<Cmpt> type;
 525 };
 526
 527 template<class Cmpt>
 528 class innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt> >
 529 {
 530 public:
 531
 532     typedef Vector2D<Cmpt> type;
 533 };
 534
 535 template<class Cmpt>
 536 class innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt> >
 537 {
 538 public:
 539
 540     typedef Vector2D<Cmpt> type;
 541 };
 542
 543
 544 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 545
 546 } // End namespace Foam
 547
 548 // ************************************************************************* //