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Commit b672d79c by Santiago Ospina

### Adds documentation for the CFL condition.


Signed-off-by: Santiago 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 TF cfl_condition(const GF& gf, unsigned int intorder = 1) ... ...
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