preparing release

Author: Francesco Rizzi

docs/.doctrees/burgers_2d_dirichlet.doctree

@@ -0,0 +1,117 @@
+2D Burgers (Dirichlet BCs)
+==========================
+
+This problem solves the 2D nonlinear viscous Burgers equations
+
+.. math::
+
+   \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y}  &= D \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) 
+
+   \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y}  &= D \left( \frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} \right)
+
+
+* Domain is :math:`[-1,1]^2` with homogeneous Dirichlet BC
+
+* Initial conditions are: :math:`u = v = \alpha \exp( - \frac{(x-x_0)^2+(y-y_0)^2}{\delta} )`
+
+* Default settings: :math:`\alpha = 0.5`, :math:`\delta = 0.15`, :math:`x_0=0, y_0=-0.2`, :math:`D = 0.00001`
+
+Mesh
+----
+
+.. code-block:: shell
+
+   python3 pressio-demoapps/meshing_scripts/create_full_mesh_for.py \
+           --problem burgers2d_dirichlet_s<stencilSize> -n Nx Ny --outDir <destination-path>
+
+where 
+
+- ``Nx, Ny`` is the number of cells you want along :math:`x` and :math:`y` respectively
+
+- ``<stencilSize> = 3 or 5 or 7``: defines the neighboring connectivity of each cell 
+
+- ``<destination-path>`` is where you want the mesh files to be generated.
+  The script creates the directory if it does not exist.
+
+
+.. Important::
+
+  When you set the ``<stencilSize>``, keep in mind the following constraints (more on this below):
+
+  - ``InviscidFluxReconstruction::FirstOrder`` requires ``<stencilSize> >= 3``
+ 
+  - ``InviscidFluxReconstruction::Weno3`` requires ``<stencilSize> >= 5``
+  
+  - ``InviscidFluxReconstruction::Weno5`` requires ``<stencilSize> >= 7``
+
+.. Currently, the viscous reconstruction uses a three-point stencil, so it is always supported.
+
+
+C++ synopsis
+------------
+
+.. code-block:: c++
+
+   #include "pressiodemoapps/advection_diffusion2d.hpp"
+   // ...
+   namespace pda = pressiodemoapps;
+
+   const auto meshObj = pda::load_cellcentered_uniform_mesh_eigen("path-to-mesh");
+
+   const auto inviscidScheme = pda::InviscidFluxReconstruction::FirstOrder; // or Weno3, Weno5
+   const auto viscousScheme  = pda::ViscousFluxReconstruction::FirstOrder;  // must be FirstOrder
+
+   // A. constructor for problem using default values
+   {
+     const auto probId = pda::AdvectionDiffusion2d::BurgersDirichlet;
+     auto problem = pda::create_problem_eigen(meshObj, probId, inviscidScheme, viscousScheme);
+   }
+
+   // B. setting custom coefficients
+   {
+     using scalar_type = typename decltype(meshObj)::scalar_t;
+     const auto alpha  = /* something */;
+     const auto delta  = /* something */;
+     const auto D      = /* something */;
+     const auto x0     = /* something */;
+     const auto y0     = /* something */;
+     auto problem = pda::create_dirichlet_burgers_2d_problem_eigen(meshObj, inviscidScheme, 
+                                                                   viscousScheme, alpha, 
+                                                                   delta, D, x0, y0)
+   }
+
+Python synopsis
+---------------
+
+.. code-block:: py
+
+   import pressiodemoapps as pda
+
+   meshObj = pda.load_cellcentered_uniform_mesh("path-to-mesh")
+
+   inviscidScheme = pda.InviscidFluxReconstruction.FirstOrder; # or Weno3, Weno5
+   viscousScheme  = pda.ViscousFluxReconstruction.FirstOrder;  # must be FirstOrder
+
+   # A. constructor for problem using default values
+   probId  = pda.AdvectionDiffusion2d.BurgersPeriodic
+   problem = pda.create_problem(meshObj, probId, inviscidScheme, viscousScheme)
+
+   # B. setting custom coefficients
+   alpha  = # something 
+   delta  = # something 
+   D      = # something 
+   x0     = # something 
+   y0     = # something
+   problem = pda.create_dirichlet_burgers_2d_problem(meshObj, inviscidScheme, 
+                                                     viscousScheme, alpha, 
+                                                     delta, D, x0, y0)
+
+
+
+Notes:
+------
+
+.. important::
+
+   Note that we currently support only first order *viscous* 
+   flux reconstruction, which leads to a second-order scheme.

docs/.doctrees/burgers_2d_periodic.doctree

@@ -1,18 +1,18 @@
-2D Burgers
-==========
-TODO: Add Initial conditions and parameters. Fix code blocks.
+2D Burgers (Periodic BCs)
+=========================
 
-This problem solves the 2D Burgers equations. We consider a two-dimensional nonlinear viscous Burgers equations
+This problem solves the 2D nonlinear viscous Burgers equations
 
 .. math::
 
-   \frac{\partial u}{\partial t} + u \nabla u = D \nabla^2 u
+   \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y}  &= D \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) 
 
-with:
+   \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y}  &= D \left( \frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} \right)
 
-* Domain is :math:`[0,1]^2` with periodic BC
 
-* initial condition is: :math:`u = \alpha \exp( - \frac{(x-x_0)^2+(y-y_0)^2}{\delta} )`
+* Domain is :math:`[-1,1]^2` with periodic BC
+
+* Initial conditions are: :math:`u = v = \alpha \exp( - \frac{(x-x_0)^2+(y-y_0)^2}{\delta} )`
 
 * Default settings: :math:`\alpha = 0.5`, :math:`\delta = 0.15`, :math:`x_0=0, y_0=-0.2`, :math:`D = 0.00001`
 
@@ -22,7 +22,7 @@ Mesh
 .. code-block:: shell
 
    python3 pressio-demoapps/meshing_scripts/create_full_mesh_for.py \
-           --problem burgers2d_s<stencilSize> -n Nx Ny --outDir <destination-path>
+           --problem burgers2d_periodic_s<stencilSize> -n Nx Ny --outDir <destination-path>
 
 where 
 
@@ -63,7 +63,7 @@ C++ synopsis
 
    // A. constructor for problem using default values
    {
-     const auto probId = pda::AdvectionDiffusion2d::Burgers;
+     const auto probId = pda::AdvectionDiffusion2d::BurgersPeriodic;
      auto problem = pda::create_problem_eigen(meshObj, probId, inviscidScheme, viscousScheme);
    }
 
@@ -75,8 +75,9 @@ C++ synopsis
      const auto D      = /* something */;
      const auto x0     = /* something */;
      const auto y0     = /* something */;
-     auto problem = pda::create_burgers_2d_problem_eigen(meshObj, inviscidScheme, viscousScheme,
-                                                         alpha, delta, D, x0, y0)
+     auto problem = pda::create_periodic_burgers_2d_problem_eigen(meshObj, inviscidScheme, 
+                                                                  viscousScheme, alpha, 
+                                                                  delta, D, x0, y0)
    }
 
 Python synopsis
@@ -92,17 +93,18 @@ Python synopsis
    viscousScheme  = pda.ViscousFluxReconstruction.FirstOrder;  # must be FirstOrder
 
    # A. constructor for problem using default values
-   probId  = pda.AdvectionDiffusion2d::Burgers
-   problem = pda.create_problem(meshObj, probId, scheme)
+   probId  = pda.AdvectionDiffusion2d.BurgersPeriodic
+   problem = pda.create_problem(meshObj, probId, inviscidScheme, viscousScheme)
 
    # B. setting custom coefficients
-   alpha  = /* something */
-   delta  = /* something */
-   D      = /* something */
-   x0     = /* something */
-   y0     = /* something */
-   problem = pda.create_burgers_2d_problem(meshObj, inviscidScheme, viscousScheme,
-                                           alpha, delta, D, x0, y0)
+   alpha  = # something 
+   delta  = # something 
+   D      = # something 
+   x0     = # something 
+   y0     = # something
+   problem = pda.create_periodic_burgers_2d_problem(meshObj, inviscidScheme, 
+                                                    viscousScheme, alpha, 
+                                                    delta, D, x0, y0)