pyro.incompressible.problems package#
Submodules#
pyro.incompressible.problems.converge module#
Initialize a smooth incompressible convergence test. Here, the velocities are initialized as
\[ \begin{align}\begin{aligned}u(x,y) = 1 - 2 \cos(2 \pi x) \sin(2 \pi y)\\v(x,y) = 1 + 2 \sin(2 \pi x) \cos(2 \pi y)\end{aligned}\end{align} \]
and the exact solution at some later time t is then
\[ \begin{align}\begin{aligned}u(x,y,t) = 1 - 2 \cos(2 \pi (x - t)) \sin(2 \pi (y - t))\\v(x,y,t) = 1 + 2 \sin(2 \pi (x - t)) \cos(2 \pi (y - t))\\p(x,y,t) = -\cos(4 \pi (x - t)) - \cos(4 \pi (y - t))\end{aligned}\end{align} \]
The numerical solution can be compared to the exact solution to measure the convergence rate of the algorithm. These initial conditions come from Minion 1996.
pyro.incompressible.problems.shear module#
Initialize the doubly periodic shear layer (see, for example, Martin and Colella, 2000, JCP, 163, 271). This is run in a unit square domain, with periodic boundary conditions on all sides. Here, the initial velocity is:
\[\begin{split}u(x,y,t=0) = \begin{cases}
\tanh(\rho_s (y - 1/4)) & \mbox{if}~ y \le 1/2 \\
\tanh(\rho_s (3/4 - y)) & \mbox{if}~ y > 1/2
\end{cases}\end{split}\]
\[v(x,y,t=0) = \delta_s \sin(2 \pi x)\]