pyro.incompressible.problems package

Contents

pyro.incompressible.problems package#

Submodules#

pyro.incompressible.problems.converge module#

Initialize a smooth incompressible convergence test. Here, the velocities are initialized as

\begin{array}{r} \begin{matrix} u (x, y) = 1 - 2 \cos (2 π x) \sin (2 π y) \\ v (x, y) = 1 + 2 \sin (2 π x) \cos (2 π y) \end{matrix} \end{array}

and the exact solution at some later time t is then

\begin{array}{r} \begin{matrix} u (x, y, t) = 1 - 2 \cos (2 π (x - t)) \sin (2 π (y - t)) \\ v (x, y, t) = 1 + 2 \sin (2 π (x - t)) \cos (2 π (y - t)) \\ p (x, y, t) = - \cos (4 π (x - t)) - \cos (4 π (y - t)) \end{matrix} \end{array}

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.converge.finalize()[source]#: print out any information to the user at the end of the run

pyro.incompressible.problems.converge.init_data(my_data, rp)[source]#: initialize the incompressible converge problem

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{array}{r} u (x, y, t = 0) = {\begin{cases} \tanh (ρ_{s} (y - 1 / 4)) & if y \leq 1 / 2 \\ \tanh (ρ_{s} (3 / 4 - y)) & if y > 1 / 2 \end{cases} \end{array}

v (x, y, t = 0) = δ_{s} \sin (2 π x)

pyro.incompressible.problems.shear.finalize()[source]#: print out any information to the user at the end of the run

pyro.incompressible.problems.shear.init_data(my_data, rp)[source]#: initialize the incompressible shear problem