pyro.incompressible_viscous.problems package#

Submodules#

pyro.incompressible_viscous.problems.cavity module#

Initialize the lid-driven cavity problem. Run on a unit square with the top wall moving to the right with unit velocity, driving the flow. The other three walls are no-slip boundary conditions. The initial velocity of the fluid is zero.

Since the length and velocity scales are both 1, the Reynolds number is 1/viscosity.

References: https://doi.org/10.1007/978-3-319-91494-7_8 https://www.fluid.tuwien.ac.at/HendrikKuhlmann?action=AttachFile&do=get&target=LidDrivenCavity.pdf

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

pyro.incompressible_viscous.problems.cavity.init_data(my_data, rp)[source]#: initialize the lid-driven cavity

pyro.incompressible_viscous.problems.converge module#

Initialize a smooth incompressible+viscous 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, for some viscosity nu, is

\begin{array}{r} \begin{matrix} u (x, y, t) = 1 - 2 \cos (2 π (x - t)) \sin (2 π (y - t)) e^{- 8 π^{2} ν t} \\ v (x, y, t) = 1 + 2 \sin (2 π (x - t)) \cos (2 π (y - t)) e^{- 8 π^{2} ν t} \\ p (x, y, t) = - (\cos (4 π (x - t)) + \cos (4 π (y - t))) e^{- 16 π^{2} ν t} \end{matrix} \end{array}

The numerical solution can be compared to the exact solution to measure the convergence rate of the algorithm.

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

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

pyro.incompressible_viscous.problems.plot_cavity module#

pyro.incompressible_viscous.problems.plot_cavity.get_args()[source]#

pyro.incompressible_viscous.problems.plot_cavity.makeplot(plotfile_name, outfile, Reynolds, streamline_density)[source]#: plot the velocity magnitude and streamlines

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

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

pyro.incompressible_viscous.problems package

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