\frac{d \textbf{x}_i}{dt} =\textbf{u}(\textbf{x}_i)
@f]
-where $\textbf{x}_i$ is the postion of particle $i$. In the present step,
-this ODE is solved using the explicit Euler method. The resulting scheme is:
+where $\textbf{x}_i$ is the postion of particle $i$ and $\textbf{u}_i$ its velocity.
+In the present step, this ODE is solved using the explicit Euler method. The resulting scheme is:
@f[
\textbf{x}_{i}^{t+\Delta t} = \textbf{x}_{i}^{t} + \Delta t \; \textbf{u}(\textbf{x}_{i}^{t})
@f]
We note that much greater accuracy could be obtained by using a fourth
order Runge-Kutta method or another appropriate scheme for the time integration
-of the motion of the particles. However, this does not alter which capacities
-are displayed in the present step.
+of the motion of the particles.
<h3>Particles in deal.II</h3>
line, the program will try to read the file "parameters.prm" by default, and
will execute the two dimensional version of the code.
-Regardless of the specific parameter file name, if the specified file does not
-exist when you execute the program you will get an exception that no such file
-can be found:
-
-@code
-----------------------------------------------------
-Exception on processing:
-
---------------------------------------------------------
-An error occurred in line <74> of file <../source/base/parameter_acceptor.cc> in function
- static void dealii::ParameterAcceptor::initialize(const std::string &, const std::string &, const ParameterHandler::OutputStyle, dealii::ParameterHandler &)
-The violated condition was:
- false
-Additional information:
- You specified <parameters.prm> as input parameter file, but it does not exist. We created it for you.
---------------------------------------------------------
-
-Aborting!
-----------------------------------------------------
-@endcode
-
-However, as the error message already states, the code that triggers the
-exception will also generate the specified file ("`parameters.prm`" in this case).
-
On any number of core, the simulation output will look like:
@code
this case the particles would need to have additional properties such as their mass,
and their diameter.
- Coupling to a flow solver. This step could be straightforwardly coupled to any parallel
-steps in which the Stokes or the Navier-Stokes equations are solved (e.g. step-57)
+steps in which the Stokes (step-32, step-70) or the Navier-Stokes equations are solved (e.g. step-57)