diff --git a/pyro/incompressible/problems/converge.py b/pyro/incompressible/problems/converge.py index 6d1e810fa..224d4d29a 100644 --- a/pyro/incompressible/problems/converge.py +++ b/pyro/incompressible/problems/converge.py @@ -19,7 +19,8 @@ p(x,y,t) = -\cos(4 \pi (x - t)) - \cos(4 \pi (y - t)) The numerical solution can be compared to the exact solution to -measure the convergence rate of the algorithm. +measure the convergence rate of the algorithm. These initial +conditions come from Minion 1996. """ diff --git a/pyro/incompressible/problems/shear.py b/pyro/incompressible/problems/shear.py index e2ce51da7..ca1598019 100644 --- a/pyro/incompressible/problems/shear.py +++ b/pyro/incompressible/problems/shear.py @@ -2,15 +2,18 @@ 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:: +initial velocity is: - / tanh(rho_s (y-0.25)) if y <= 0.5 - u(x,y,t=0) = < - \ tanh(rho_s (0.75-y)) if y > 0.5 +.. math:: - v(x,y,t=0) = delta_s sin(2 pi x) + 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} +.. math:: + v(x,y,t=0) = \delta_s \sin(2 \pi x) """ diff --git a/pyro/incompressible_viscous/problems/shear.py b/pyro/incompressible_viscous/problems/shear.py index e2ce51da7..ca1598019 100644 --- a/pyro/incompressible_viscous/problems/shear.py +++ b/pyro/incompressible_viscous/problems/shear.py @@ -2,15 +2,18 @@ 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:: +initial velocity is: - / tanh(rho_s (y-0.25)) if y <= 0.5 - u(x,y,t=0) = < - \ tanh(rho_s (0.75-y)) if y > 0.5 +.. math:: - v(x,y,t=0) = delta_s sin(2 pi x) + 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} +.. math:: + v(x,y,t=0) = \delta_s \sin(2 \pi x) """