@@ -16,7 +16,13 @@ We implemented a few examples to display how Dune-MMesh can be used in different
examples/poroelasticity
examples/twophase
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examples/grids/grids
Some examples for the creation of grid files can be found in :ref:`grids`.
.. [CMR+18] C. Chalons, J. Magiera, C. Rohde, M. Wiebe. A Finite-Volume Tracking Scheme for Two-Phase Compressible Flow. Theory, Numerics and Applications of Hyperbolic Problems I, pp. 309--322, 2018.
"We use a .msh file that contains an interface $\\Gamma = [0.25, 0.75] \\times {0.5}$ embedded in a domain $\\Omega = [0,1]^2$."
"We use the [horizontal](grids/horizontal.rst) grid file that contains an interface $\\Gamma = [0.25, 0.75] \\times {0.5}$ embedded in a domain $\\Omega = [0,1]^2$."
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# Coupling to the interface
This is an example of how to solve coupled problems on the bulk and interface grid.
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## Grid creation
We use a .msh file that contains an interface $\Gamma = [0.25, 0.75] \times {0.5}$ embedded in a domain $\Omega = [0,1]^2$.
We use the [horizontal](grids/horizontal.rst) grid file that contains an interface $\Gamma = [0.25, 0.75] \times {0.5}$ embedded in a domain $\Omega = [0,1]^2$.
"We use a .msh file that contains an interface $\\Gamma = {0.5} \\times [0, 1]$ embedded in a domain $\\Omega = [0,1]^2$ and construct an _adaptive_ leaf grid view."
"We use the [vertical](grids/vertical.rst) grid file that contains an interface $\\Gamma = {0.5} \\times [0, 1]$ embedded in a domain $\\Omega = [0,1]^2$ and construct an _adaptive_ leaf grid view."
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# Moving and adapting
This is an example of how to move the interface and adapt the mesh.
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## Grid creation
We use a .msh file that contains an interface $\Gamma = {0.5} \times [0, 1]$ embedded in a domain $\Omega = [0,1]^2$ and construct an _adaptive_ leaf grid view.
We use the [vertical](grids/vertical.rst) grid file that contains an interface $\Gamma = {0.5} \times [0, 1]$ embedded in a domain $\Omega = [0,1]^2$ and construct an _adaptive_ leaf grid view.
Now, we can start with the time loop. We need to set the `fem.adaptation.method` parameter to `callback` in order to use the adaptation startegy of Dune-MMesh.
"Here, $\\nu_i, i=1,2,$ are the kinematic viscositities and $\\rho_i, i=1,2,$ the densities of the two phases, $g$ is the gravity, $\\sigma$ is the surface tension and $\\kappa$ is the signed mean curvature of the interface.\n",
"\n",
"Now, we use Dune-MMesh to compute the result of a rising bubble."
"Now, we use Dune-MMesh to compute the result of a rising bubble. Let us consider the [circle](grids/circle.rst) grid."
Here, $\nu_i, i=1,2,$ are the kinematic viscositities and $\rho_i, i=1,2,$ the densities of the two phases, $g$ is the gravity, $\sigma$ is the surface tension and $\kappa$ is the signed mean curvature of the interface.
Now, we use Dune-MMesh to compute the result of a rising bubble.
Now, we use Dune-MMesh to compute the result of a rising bubble. Let us consider the [circle](grids/circle.rst) grid.
