src/OpenFOAM/primitives/Tensor2D/Tensor2DI.H

   1 /*---------------------------------------------------------------------------*\
   2   =========                 |
   3   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   4    \\    /   O peration     |
   5     \\  /    A nd           | Copyright (C) 1991-2008 OpenCFD Ltd.
   6      \\/     M anipulation  |
   7 -------------------------------------------------------------------------------
   8 License
   9     This file is part of OpenFOAM.
  10
  11     OpenFOAM 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 2 of the License, or (at your
  14     option) any later version.
  15
  16     OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
  17     ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  18     FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  19     for more details.
  20
  21     You should have received a copy of the GNU General Public License
  22     along with OpenFOAM; if not, write to the Free Software Foundation,
  23     Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
  24
  25 \*---------------------------------------------------------------------------*/
  26
  27 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
  28
  29 namespace Foam
  30 {
  31
  32 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
  33
  34 template <class Cmpt>
  35 inline Tensor2D<Cmpt>::Tensor2D()
  36 {}
  37
  38
  39 template <class Cmpt>
  40 inline Tensor2D<Cmpt>::Tensor2D(const VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>& vs)
  41 :
  42     VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(vs)
  43 {}
  44
  45
  46 template <class Cmpt>
  47 inline Tensor2D<Cmpt>::Tensor2D(const SphericalTensor2D<Cmpt>& st)
  48 {
  49     this->v_[XX] = st.ii(); this->v_[XY] = 0;
  50     this->v_[YX] = 0; this->v_[YY] = st.ii();
  51 }
  52
  53
  54 template <class Cmpt>
  55 inline Tensor2D<Cmpt>::Tensor2D
  56 (
  57     const Cmpt txx, const Cmpt txy,
  58     const Cmpt tyx, const Cmpt tyy
  59 )
  60 {
  61     this->v_[XX] = txx; this->v_[XY] = txy;
  62     this->v_[YX] = tyx; this->v_[YY] = tyy;
  63 }
  64
  65
  66 template <class Cmpt>
  67 inline Tensor2D<Cmpt>::Tensor2D(Istream& is)
  68 :
  69     VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(is)
  70 {}
  71
  72
  73 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
  74
  75 template <class Cmpt>
  76 inline const Vector2D<Cmpt>&  Tensor2D<Cmpt>::x() const
  77 {
  78     return reinterpret_cast<const Vector2D<Cmpt>&>(this->v_[XX]);
  79 }
  80
  81 template <class Cmpt>
  82 inline const Vector2D<Cmpt>&  Tensor2D<Cmpt>::y() const
  83 {
  84     return reinterpret_cast<const Vector2D<Cmpt>&>(this->v_[YX]);
  85 }
  86
  87
  88 template <class Cmpt>
  89 inline Vector2D<Cmpt>&  Tensor2D<Cmpt>::x()
  90 {
  91     return reinterpret_cast<Vector2D<Cmpt>&>(this->v_[XX]);
  92 }
  93
  94 template <class Cmpt>
  95 inline Vector2D<Cmpt>&  Tensor2D<Cmpt>::y()
  96 {
  97     return reinterpret_cast<Vector2D<Cmpt>&>(this->v_[YX]);
  98 }
  99
 100
 101 template <class Cmpt>
 102 inline const Cmpt&  Tensor2D<Cmpt>::xx() const
 103 {
 104     return this->v_[XX];
 105 }
 106
 107 template <class Cmpt>
 108 inline const Cmpt&  Tensor2D<Cmpt>::xy() const
 109 {
 110     return this->v_[XY];
 111 }
 112
 113 template <class Cmpt>
 114 inline const Cmpt&  Tensor2D<Cmpt>::yx() const
 115 {
 116     return this->v_[YX];
 117 }
 118
 119 template <class Cmpt>
 120 inline const Cmpt&  Tensor2D<Cmpt>::yy() const
 121 {
 122     return this->v_[YY];
 123 }
 124
 125
 126 template <class Cmpt>
 127 inline Cmpt& Tensor2D<Cmpt>::xx()
 128 {
 129     return this->v_[XX];
 130 }
 131
 132 template <class Cmpt>
 133 inline Cmpt& Tensor2D<Cmpt>::xy()
 134 {
 135     return this->v_[XY];
 136 }
 137
 138 template <class Cmpt>
 139 inline Cmpt& Tensor2D<Cmpt>::yx()
 140 {
 141     return this->v_[YX];
 142 }
 143
 144 template <class Cmpt>
 145 inline Cmpt& Tensor2D<Cmpt>::yy()
 146 {
 147     return this->v_[YY];
 148 }
 149
 150
 151 template <class Cmpt>
 152 inline Tensor2D<Cmpt> Tensor2D<Cmpt>::T() const
 153 {
 154     return Tensor2D<Cmpt>
 155     (
 156         xx(), yx(),
 157         xy(), yy()
 158     );
 159 }
 160
 161
 162 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 163
 164 template <class Cmpt>
 165 inline void Tensor2D<Cmpt>::operator=(const SphericalTensor2D<Cmpt>& st)
 166 {
 167     this->v_[XX] = st.ii(); this->v_[XY] = 0;
 168     this->v_[YX] = 0; this->v_[YY] = st.ii();
 169 }
 170
 171
 172
 173 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 174
 175 //- Inner-product between two tensors
 176 template <class Cmpt>
 177 inline typename innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt> >::type
 178 operator&(const Tensor2D<Cmpt>& t1, const Tensor2D<Cmpt>& t2)
 179 {
 180     return Tensor2D<Cmpt>
 181     (
 182         t1.xx()*t2.xx() + t1.xy()*t2.yx(),
 183         t1.xx()*t2.xy() + t1.xy()*t2.yy(),
 184
 185         t1.yx()*t2.xx() + t1.yy()*t2.yx(),
 186         t1.yx()*t2.xy() + t1.yy()*t2.yy()
 187     );
 188 }
 189
 190 //- Inner-product between a tensor and a vector
 191 template <class Cmpt>
 192 inline typename innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt> >::type
 193 operator&(const Tensor2D<Cmpt>& t, const Vector2D<Cmpt>& v)
 194 {
 195     return Vector2D<Cmpt>
 196     (
 197         t.xx()*v.x() + t.xy()*v.y(),
 198         t.yx()*v.x() + t.yy()*v.y()
 199     );
 200 }
 201
 202 //- Inner-product between a vector and a tensor
 203 template <class Cmpt>
 204 inline typename innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt> >::type
 205 operator&(const Vector2D<Cmpt>& v, const Tensor2D<Cmpt>& t)
 206 {
 207     return Vector2D<Cmpt>
 208     (
 209         v.x()*t.xx() + v.y()*t.yx(),
 210         v.x()*t.xy() + v.y()*t.yy()
 211     );
 212 }
 213
 214 //- Outer-product between two vectors
 215 template <class Cmpt>
 216 inline typename outerProduct<Vector2D<Cmpt>, Vector2D<Cmpt> >::type
 217 operator*(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
 218 {
 219     return Tensor2D<Cmpt>
 220     (
 221         v1.x()*v2.x(), v1.x()*v2.y(),
 222         v1.y()*v2.x(), v1.y()*v2.y()
 223     );
 224 }
 225
 226
 227 //- Return the trace of a tensor
 228 template <class Cmpt>
 229 inline Cmpt tr(const Tensor2D<Cmpt>& t)
 230 {
 231     return t.xx() + t.yy();
 232 }
 233
 234
 235 //- Return the spherical part of a tensor
 236 template <class Cmpt>
 237 inline SphericalTensor2D<Cmpt> sph(const Tensor2D<Cmpt>& t)
 238 {
 239     return 0.5*tr(t);
 240 }
 241
 242
 243 //- Return the symmetric part of a tensor
 244 template <class Cmpt>
 245 inline Tensor2D<Cmpt> symm(const Tensor2D<Cmpt>& t)
 246 {
 247     return Tensor2D<Cmpt>
 248     (
 249         t.xx(), 0.5*(t.xy() + t.yx()),
 250         0.5*(t.yx() + t.xy()), t.yy()
 251     );
 252 }
 253
 254 //- Return the twice the symmetric part of a tensor
 255 template <class Cmpt>
 256 inline Tensor2D<Cmpt> twoSymm(const Tensor2D<Cmpt>& t)
 257 {
 258     return Tensor2D<Cmpt>
 259     (
 260         t.xx() + t.xx(), t.xy() + t.yx(),
 261         t.yx() + t.xy(), t.yy() + t.yy()
 262     );
 263 }
 264
 265 //- Return the skew-symmetric part of a tensor
 266 template <class Cmpt>
 267 inline Tensor2D<Cmpt> skew(const Tensor2D<Cmpt>& t)
 268 {
 269     return Tensor2D<Cmpt>
 270     (
 271         0.0, 0.5*(t.xy() - t.yx()),
 272         0.5*(t.yx() - t.xy()), 0.0
 273     );
 274 }
 275
 276
 277 //- Return the deviatoric part of a tensor
 278 template <class Cmpt>
 279 inline Tensor2D<Cmpt> dev(const Tensor2D<Cmpt>& t)
 280 {
 281     return t - SphericalTensor2D<Cmpt>::oneThirdI*tr(t);
 282 }
 283
 284
 285 //- Return the deviatoric part of a tensor
 286 template <class Cmpt>
 287 inline Tensor2D<Cmpt> dev2(const Tensor2D<Cmpt>& t)
 288 {
 289     return t - SphericalTensor2D<Cmpt>::twoThirdsI*tr(t);
 290 }
 291
 292
 293 //- Return the determinant of a tensor
 294 template <class Cmpt>
 295 inline Cmpt det(const Tensor2D<Cmpt>& t)
 296 {
 297     return(t.xx()*t.yy() - t.xy()*t.yx());
 298 }
 299
 300
 301 //- Return the cofactor tensor of a tensor
 302 template <class Cmpt>
 303 inline Tensor2D<Cmpt> cof(const Tensor2D<Cmpt>& t)
 304 {
 305     return Tensor2D<Cmpt>
 306     (
 307         t.yy(), -t.xy(),
 308        -t.yx(),  t.xx()
 309     );
 310 }
 311
 312
 313 //- Return the inverse of a tensor given the determinant
 314 template <class Cmpt>
 315 inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt dett)
 316 {
 317     return cof(t)/dett;
 318 }
 319
 320
 321 //- Return the inverse of a tensor
 322 template <class Cmpt>
 323 inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t)
 324 {
 325     return inv(t, det(t));
 326 }
 327
 328
 329 //- Return the 1st invariant of a tensor
 330 template <class Cmpt>
 331 inline Cmpt invariantI(const Tensor2D<Cmpt>& t)
 332 {
 333     return tr(t);
 334 }
 335
 336
 337 //- Return the 2nd invariant of a tensor
 338 template <class Cmpt>
 339 inline Cmpt invariantII(const Tensor2D<Cmpt>& t)
 340 {
 341     return
 342     (
 343         0.5*sqr(tr(t))
 344       - 0.5*
 345         (
 346            t.xx()*t.xx() + t.xy()*t.xy()
 347          + t.yx()*t.yx() + t.yy()*t.yy()
 348         )
 349     );
 350 }
 351
 352
 353 //- Return the 3rd invariant of a tensor
 354 template <class Cmpt>
 355 inline Cmpt invariantIII(const Tensor2D<Cmpt>& t)
 356 {
 357     return det(t);
 358 }
 359
 360
 361
 362
 363 template <class Cmpt>
 364 inline Tensor2D<Cmpt>
 365 operator+(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 366 {
 367     return Tensor2D<Cmpt>
 368     (
 369         st1.ii() + t2.xx(), t2.xy(),
 370         t2.yx(),            st1.ii() + t2.yy()
 371     );
 372 }
 373
 374
 375 template <class Cmpt>
 376 inline Tensor2D<Cmpt>
 377 operator+(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 378 {
 379     return Tensor2D<Cmpt>
 380     (
 381         t1.xx() + st2.ii(), t1.xy(),
 382         t1.yx(),            t1.yy() + st2.ii()
 383     );
 384 }
 385
 386
 387 template <class Cmpt>
 388 inline Tensor2D<Cmpt>
 389 operator-(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 390 {
 391     return Tensor2D<Cmpt>
 392     (
 393         st1.ii() - t2.xx(), -t2.xy(),
 394        -t2.yx(),             st1.ii() - t2.yy()
 395     );
 396 }
 397
 398
 399 template <class Cmpt>
 400 inline Tensor2D<Cmpt>
 401 operator-(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 402 {
 403     return Tensor2D<Cmpt>
 404     (
 405         t1.xx() - st2.ii(), t1.xy(),
 406         t1.yx(),            t1.yy() - st2.ii()
 407     );
 408 }
 409
 410
 411 //- Inner-product between a spherical tensor and a tensor
 412 template <class Cmpt>
 413 inline Tensor2D<Cmpt>
 414 operator&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 415 {
 416     return Tensor2D<Cmpt>
 417     (
 418         st1.ii()*t2.xx(),
 419         st1.ii()*t2.xy(),
 420                           st1.ii()*t2.yx(),
 421                           st1.ii()*t2.yy()
 422     );
 423 }
 424
 425
 426 //- Inner-product between a tensor and a spherical tensor
 427 template <class Cmpt>
 428 inline Tensor2D<Cmpt>
 429 operator&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 430 {
 431     return Tensor2D<Cmpt>
 432     (
 433         t1.xx()*st2.ii(),
 434                           t1.xy()*st2.ii(),
 435
 436         t1.yx()*st2.ii(),
 437                           t1.yy()*st2.ii()
 438     );
 439 }
 440
 441
 442 //- Double-dot-product between a spherical tensor and a tensor
 443 template <class Cmpt>
 444 inline Cmpt
 445 operator&&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
 446 {
 447     return(st1.ii()*t2.xx() + st1.ii()*t2.yy());
 448 }
 449
 450
 451 //- Double-dot-product between a tensor and a spherical tensor
 452 template <class Cmpt>
 453 inline Cmpt
 454 operator&&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
 455 {
 456     return(t1.xx()*st2.ii() + t1.yy()*st2.ii());
 457 }
 458
 459
 460 template<class Cmpt>
 461 class typeOfSum<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
 462 {
 463 public:
 464
 465     typedef Tensor2D<Cmpt> type;
 466 };
 467
 468 template<class Cmpt>
 469 class typeOfSum<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
 470 {
 471 public:
 472
 473     typedef Tensor2D<Cmpt> type;
 474 };
 475
 476
 477 template<class Cmpt>
 478 class innerProduct<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
 479 {
 480 public:
 481
 482     typedef Tensor2D<Cmpt> type;
 483 };
 484
 485 template<class Cmpt>
 486 class innerProduct<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
 487 {
 488 public:
 489
 490     typedef Tensor2D<Cmpt> type;
 491 };
 492
 493
 494 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 495
 496 } // End namespace Foam
 497
 498 // ************************************************************************* //