Commit b672d79c authored by Santiago Ospina's avatar Santiago Ospina

Adds documentation for the CFL condition.

Signed-off-by: Santiago Ospina De Los Ríos's avatarSantiago Ospina <santiago.ospina@iup.uni-heidelberg.de>
parent 375f55c9
......@@ -9,27 +9,35 @@ namespace Dune{
namespace Dorie{
/**
* @brief Computes the CFL condition for a grid function representing a
* velocity field. In particular, the return value is the
* suggested timestep for the lowest CFL ratio for each cell:
* @brief Computes the CFL-condition (\f$\mathcal{CFL}\f$) for a grid
* function representing a velocity field. In particular, the
* return value is the suggested timestep for the lowest CFL
* ratio for each cell:
*
* @f{eqnarray*}{
* CFL = \min_{T\in\mathcal{T}_h}{||\beta||^{-1}_{L^inf(T)h^T} \\
* \delta t \lt \rho CFL
* \mathcal{CFL} = \min_{T\in\mathcal{T}_h} ||\beta||^{-1}_{[L^\infty(T)]^d}h_T
* @f}
* where \f$\mathcal{T}_h\f$ is triangulation, \f$\beta\f$ the
* velocity field, and \f$h_T\f$ the diameter of the cell
* \f$T\in \mathcal{T}_h\f$.
* As is usual with the CFL-condition, one can restrict the time
* step \f$\Delta t\f$ for explicit schemes using a given courant
* number \f$\varrho \le 1\f$:
*
* @f{eqnarray*}{
* \Delta t \lt \varrho \cdot \mathcal{CFL}
* @f}
* where $\rho$ is the courant number and $\beta$ is the velocity
* field.
*
* @param[in] gf Grid function representing the veolcity field
* $\beta$.
* \f$\beta\f$.
* @param[in] intorder The integration order. This value determines the
* quadrature points to evaluate
* $||\beta||_{L^inf(T)h^T}$.
* \f$||\beta||_{[L^\infty(T)]^d}h_T\f$.
*
* @tparam GF The grid function type.
* @tparam TF The time field. Type to represent time values.
*
* @return { description_of_the_return_value }
* @return The CFL-condition (\f$\mathcal{CFL}\f$)
*/
template<class GF, class TF = double>
TF cfl_condition(const GF& gf, unsigned int intorder = 1)
......
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