#include <include/ryujin/euler/initial_state_becker_solution.h>

Inheritance diagram for ryujin::EulerInitialStates::BeckerSolution< Description, dim, Number >:

[legend]

Collaboration diagram for ryujin::EulerInitialStates::BeckerSolution< Description, dim, Number >:

[legend]

Public Types
using	HyperbolicSystem = typename Description::HyperbolicSystem

using	View = typename HyperbolicSystem::template View< dim, Number >

using	state_type = typename View::state_type

Public Types inherited from ryujin::InitialState< Description, dim, Number >
using	HyperbolicSystem = typename HyperbolicDescription::HyperbolicSystem

using	View = typename HyperbolicSystem::template View< dim, Number >

using	state_type = typename View::state_type

using	initial_precomputed_type = typename View::initial_precomputed_type

Public Member Functions
	BeckerSolution (const HyperbolicSystem &hyperbolic_system, const std::string &subsection)

state_type	compute (const dealii::Point< dim > &point, Number t) final

Public Member Functions inherited from ryujin::InitialState< Description, dim, Number >
	InitialState (const std::string &name, const std::string &subsection)

virtual initial_precomputed_type	initial_precomputations (const dealii::Point< dim > &)

Detailed Description

template<typename Description, int dim, typename Number>
class ryujin::EulerInitialStates::BeckerSolution< Description, dim, Number >

The Becker solution.

An analytic solution of the compressible Navier-Stokes system as described in [1].

The initial state is a 1D stationary, viscous shock that is expanded to 2D/3D if necessary with an additional Galilei transform to add a velocity. Internally, the routine solves the equation

\begin{equation} x = \frac{2}{\gamma+1} \frac{\kappa}{m_0 c_v} \Big\{\frac{v_0}{v_0-v_1}\log\Big(\frac{v_0-v(x)}{v_0-v_{01}}\Big) - \frac{v_1}{v_0-v_1}\log\Big(\frac{v(x)-v_1}{v_{01}-v_1}\Big)\Big\}. \end{equation}

to high accuracy to recover the function \(v(x)\). This information is then used to compute density and internal energy as follows:

\begin{equation} \rho(x) = \frac{m_0}{v(x)}, \qquad e(x) = \frac{1}{2\gamma}\Big(\frac{\gamma+1}{\gamma-1}v_{01}^2 - v^2(x)\Big). \end{equation}

For details see the dicussion in [13] Section 7.2.

Note: This class returns the analytic solution as a function of time t and position x.

Definition at line 46 of file initial_state_becker_solution.h.