--- /dev/null
+New: The Rayleigh--Kothe vortex has been extracted
+from step-68 and is now availabe as the new class
+Functions::RayleighKotheVortex.
+<br>
+(Bruno Blais, Peter Munch, 2023/08/20)
#include <deal.II/base/bounding_box.h>
#include <deal.II/base/conditional_ostream.h>
#include <deal.II/base/discrete_time.h>
+#include <deal.II/base/function_lib.h>
#include <deal.II/base/mpi.h>
#include <deal.II/base/parameter_acceptor.h>
#include <deal.II/base/timer.h>
- // @sect3{Velocity profile}
-
- // The velocity profile is provided as a Function object.
- // This function is hard-coded within
- // the example.
- template <int dim>
- class Vortex : public Function<dim>
- {
- public:
- Vortex()
- : Function<dim>(dim)
- {}
-
-
- virtual void vector_value(const Point<dim> &point,
- Vector<double> &values) const override;
- };
-
-
- // The velocity profile for the Rayleigh-Kothe vertex is time-dependent.
- // Consequently, the current time in the
- // simulation (t) must be gathered from the Function object.
- template <int dim>
- void Vortex<dim>::vector_value(const Point<dim> &point,
- Vector<double> &values) const
- {
- const double T = 4;
- const double t = this->get_time();
-
- const double px = numbers::PI * point(0);
- const double py = numbers::PI * point(1);
- const double pt = numbers::PI / T * t;
-
- values[0] = -2 * cos(pt) * pow(sin(px), 2) * sin(py) * cos(py);
- values[1] = 2 * cos(pt) * pow(sin(py), 2) * sin(px) * cos(px);
- if (dim == 3)
- {
- values[2] = 0;
- }
- }
-
-
-
// @sect3{The <code>ParticleTracking</code> class declaration}
// We are now ready to introduce the main class of our tutorial program.
MappingQ1<dim> mapping;
LinearAlgebra::distributed::Vector<double> velocity_field;
- Vortex<dim> velocity;
+ Functions::RayleighKotheVortex<dim> velocity;
ConditionalOStream pcout;
, background_triangulation(mpi_communicator)
, fluid_dh(background_triangulation)
, fluid_fe(FE_Q<dim>(par.velocity_degree) ^ dim)
+ , velocity(4.0)
, pcout(std::cout, Utilities::MPI::this_mpi_process(mpi_communicator) == 0)
, interpolated_velocity(interpolated_velocity)
const std::vector<double> coefficients;
};
+
+ /**
+ * A class that represents a time-dependent function object for a
+ * Rayleigh--Kothe vortex vector field. This is generally used as
+ * flow pattern in complex test cases for interface tracking methods
+ * (e.g., volume-of-fluid and level-set approaches) since it leads
+ * to strong rotation and elongation of the fluid @cite Blais2013.
+ *
+ * The stream function $\Psi$ of this Rayleigh-Kothe vortex is defined as:
+@f[
+\Psi = \frac{1}{\pi} \sin^2 (\pi x) \sin^2 (\pi y) \cos \left( \pi \frac{t}{T}
+\right)
+@f]
+ * where $T$ is half the period of the flow. The velocity profile in 2D
+($\textbf{u}=[u,v]^T$) is :
+@f{eqnarray*}{
+ u &=& - \frac{\partial\Psi}{\partial y} = -2 \sin^2 (\pi x) \sin (\pi y)
+\cos (\pi y) \cos \left( \pi \frac{t}{T} \right)\\ v &=&
+\frac{\partial\Psi}{\partial x} = 2 \cos(\pi x) \sin(\pi x) \sin^2 (\pi y) \cos
+\left( \pi \frac{t}{T} \right)
+@f}
+ * where $T$ is half the period of the flow.
+ *
+ * The velocity profile is illustrated in the following animation:
+ *
+@htmlonly
+<p align="center">
+ <iframe width="560" height="500"
+src="https://www.youtube.com/embed/m6hQm7etji8" frameborder="0"
+ allow="accelerometer; autoplay; encrypted-media; gyroscope;
+picture-in-picture" allowfullscreen></iframe>
+ </p>
+@endhtmlonly
+ *
+ * It can be seen that this velocity reverses periodically due to the term
+ * $\cos \left( \pi \frac{t}{T} \right)$ and that material will end up at its
+ * starting position after every period of length $t=2T$.
+ *
+ * @note This class is only implemented for 2D and 3D. In 3D, the
+ * third component is set to zero.
+ *
+ * @ingroup functions
+ */
+ template <int dim>
+ class RayleighKotheVortex : public Function<dim>
+ {
+ public:
+ /**
+ * Constructor.
+ */
+ RayleighKotheVortex(const double T = 1.0);
+
+ /**
+ * Return all components of a vector-valued function at a given point.
+ */
+ virtual void
+ vector_value(const Point<dim> &point,
+ Vector<double> &values) const override;
+
+ private:
+ /**
+ * Half the period of the flow.
+ */
+ const double T;
+ };
+
#ifndef DOXYGEN
sizeof(coefficients);
}
+ template <int dim>
+ RayleighKotheVortex<dim>::RayleighKotheVortex(const double T)
+ : Function<dim>(dim)
+ , T(T)
+ {
+ AssertThrow(dim > 1, ExcNotImplemented());
+ }
+
+
+ template <int dim>
+ void
+ RayleighKotheVortex<dim>::vector_value(const Point<dim> &point,
+ Vector<double> &values) const
+ {
+ const double pi_x = numbers::PI * point(0);
+ const double pi_y = numbers::PI * point(1);
+ const double pi_t = numbers::PI / T * this->get_time();
+
+ values[0] = -2 * std::cos(pi_t) * std::pow(std::sin(pi_x), 2) *
+ std::sin(pi_y) * std::cos(pi_y);
+ values[1] = +2 * std::cos(pi_t) * std::pow(std::sin(pi_y), 2) *
+ std::sin(pi_x) * std::cos(pi_x);
+
+ if (dim == 3)
+ values[2] = 0;
+ }
// explicit instantiations
template class Polynomial<1>;
template class Polynomial<2>;
template class Polynomial<3>;
+ template class RayleighKotheVortex<1>;
+ template class RayleighKotheVortex<2>;
+ template class RayleighKotheVortex<3>;
} // namespace Functions
DEAL_II_NAMESPACE_CLOSE
#include <deal.II/base/bounding_box.h>
#include <deal.II/base/conditional_ostream.h>
#include <deal.II/base/discrete_time.h>
+#include <deal.II/base/function_lib.h>
#include <deal.II/base/mpi.h>
#include <deal.II/base/parameter_acceptor.h>
#include <deal.II/base/timer.h>
};
- template <int dim>
- class Vortex : public Function<dim>
- {
- public:
- Vortex()
- : Function<dim>(dim)
- {}
-
-
- virtual void
- vector_value(const Point<dim> &point,
- Vector<double> &values) const override;
- };
-
-
- template <int dim>
- void
- Vortex<dim>::vector_value(const Point<dim> &point,
- Vector<double> &values) const
- {
- const double T = 4;
- const double t = this->get_time();
-
- const double px = numbers::PI * point(0);
- const double py = numbers::PI * point(1);
- const double pt = numbers::PI / T * t;
-
- values[0] = -2 * cos(pt) * pow(sin(px), 2) * sin(py) * cos(py);
- values[1] = 2 * cos(pt) * pow(sin(py), 2) * sin(px) * cos(px);
- if (dim == 3)
- {
- values[2] = 0;
- }
- }
-
-
template <int dim>
class ParticleTracking
MappingQ1<dim> mapping;
LinearAlgebra::distributed::Vector<double> velocity_field;
- Vortex<dim> velocity;
+ Functions::RayleighKotheVortex<dim> velocity;
ConditionalOStream pcout;
, background_triangulation(mpi_communicator)
, fluid_dh(background_triangulation)
, fluid_fe(FE_Q<dim>(par.velocity_degree), dim)
+ , velocity(4.0)
, pcout(std::cout,
debug && Utilities::MPI::this_mpi_process(mpi_communicator) == 0)
, interpolated_velocity(interpolated_velocity)
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