Lines Matching full:pi
393 u = 1 - cos(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t)
394 v = 1 + sin(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)
395 p = -1/4 [cos(2 \pi(x - t)) + cos(2 \pi(y - t))] exp(-4 \pi^2 \nu t)
397 …f = <\nu \pi^2 exp(-2\nu \pi^2 t) cos(\pi(x-t)) sin(\pi(y-t)), -\nu \pi^2 exp(-2\nu \pi^2 t) sin(\…
398 Q = 3 + sin(\pi(x-y)) exp(-2\nu \pi^2 t)
402 …\nabla \cdot u = \pi sin(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t) - \pi sin(\pi(x - t)) sin…
405 …= <-\pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t)) - 2\pi cos(\pi(x - t)) …
406 …\pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t)) - 2\pi sin(\pi(x - t)) cos(…
407 …+ < \pi (1 - cos(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t)) sin(\pi(x - t)) sin(\pi(y - t)) …
408 …\pi (1 - cos(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t)) cos(\pi(x - t)) cos(\pi(y - t)) exp(…
409 …+ <-\pi (1 + sin(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)) cos(\pi(x - t)) cos(\pi(y - t)) …
410 …-\pi (1 + sin(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)) sin(\pi(x - t)) sin(\pi(y - t)) exp…
411 + <-2\pi^2 cos(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t),
412 2\pi^2 sin(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)>
413 + < \pi/2 sin(2\pi(x - t)) exp(-4 \pi^2 \nu t),
414 \pi/2 sin(2\pi(y - t)) exp(-4 \pi^2 \nu t)>
415 …= <-\pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t)) - 2\pi cos(\pi(x - t)) …
416 …\pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t)) - 2\pi sin(\pi(x - t)) cos(…
417 + < \pi sin(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t),
418 \pi cos(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)>
419 + <-\pi cos(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t),
420 -\pi sin(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t)>
421 + <-\pi/2 sin(2\pi(x - t)) exp(-4 \pi^2 \nu t),
422 -\pi/2 sin(2\pi(y - t)) exp(-4 \pi^2 \nu t)>
423 + <-2\pi^2 cos(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t),
424 2\pi^2 sin(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)>
425 + < \pi/2 sin(2\pi(x - t)) exp(-4 \pi^2 \nu t),
426 \pi/2 sin(2\pi(y - t)) exp(-4 \pi^2 \nu t)>
427 = <-\pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t))) exp(-2 \pi^2 \nu t),
428 \pi (sin(\pi(x - t)) sin(\pi(y - t)) - cos(\pi(x - t)) cos(\pi(y - t))) exp(-2 \pi^2 \nu t)>
429 + < \pi sin(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t),
430 \pi cos(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t)>
431 + <-\pi cos(\pi(x - t)) cos(\pi(y - t)) exp(-2 \pi^2 \nu t),
432 -\pi sin(\pi(x - t)) sin(\pi(y - t)) exp(-2 \pi^2 \nu t)>
433 = < \pi cos(\pi(x - t)) cos(\pi(y - t)),
434 \pi sin(\pi(x - t)) sin(\pi(y - t))>
435 + <-\pi cos(\pi(x - t)) cos(\pi(y - t)),
436 -\pi sin(\pi(x - t)) sin(\pi(y - t))> = 0
505 = 0 + 0 - div (2\mu/Re \epsilon'(u) - pI) + rho / F^2 \hat y
605 u = \Delta Re/(2 mu) [y (1 - y) + a sin(pi y)]
608 T = y (1 - y) + a sin(pi y) + T_in
614 grad u = \Delta Re/(2 mu) <<0, 0>, <1 - 2y + a pi cos(pi y), 0>>
615 …/2 (grad u + grad u^T) = \Delta Re/(4 mu) <<0, 1 - 2y + a pi cos(pi y)>, <<1 - 2y + a pi cos(pi y)…
617 div epsilon'(u) = -\Delta Re/(2 mu) <1 + a pi^2/2 sin(pi y), 0>
620 = 0 + 0 - div (2\mu/Re \epsilon'(u) - pI) + rho / F^2 \hat y
621 …= -\Delta div <<x, (1 - 2y)/2 + a pi/2 cos(pi y)>, <<(1 - 2y)/2 + a pi/2 cos(pi y), x>> + rho / F^…
622 = -\Delta <1 - 1 - a pi^2/2 sin(pi y), 0> + rho/F^2 <0, 1>
623 = a \Delta pi^2/2 sin(pi y) <1, 0> + rho/F^2 <0, 1>
631 = 0 + c_p pth / T 0 - k/Pe div <0, 1 - 2y + a pi cos(pi y)>
632 = - k/Pe (-2 - a pi^2 sin(pi y))
633 = 2 k/Pe (1 + a pi^2/2 sin(pi y))
637 … \epsilon'(u) - p I) . n = \Delta <<x, (1 - 2y)/2 + a pi/2 cos(pi y)>, <<(1 - 2y)/2 + a pi/2 cos(p…
641 x = 0: \Delta <<0, (1 - 2y)/2>, <<(1 - 2y)/2, 0>> . <-1, 0> = <0, (2y - 1)/2 - a pi/2 cos(pi y)>
642 x = 1: \Delta <<1, (1 - 2y)/2>, <<(1 - 2y)/2, 1>> . < 1, 0> = <1, (1 - 2y)/2 + a pi/2 cos(pi y)>
791 /*f1_v = \nu[grad(u) + grad(u)^T] - pI */