Mesh generation and discretization

Namespaces
namespace	ryujin::GridGenerator
namespace	ryujin::Geometries

Classes
class	ryujin::CubicSpline
class	ryujin::Discretization< dim >
class	ryujin::Geometry< dim >
class	ryujin::Geometries::Airfoil< dim >
class	ryujin::Geometries::Annulus< dim >
class	ryujin::Geometries::Cylinder< dim >
class	ryujin::Geometries::RectangularDomain< dim >
class	ryujin::Geometries::Step< dim >
class	ryujin::Geometries::WaveTank< dim >
class	ryujin::Geometries::Wall< dim >

Enumerations
enum	ryujin::Boundary : dealii::types::boundary_id {   ryujin::do_nothing = 0 , ryujin::periodic = 1 , ryujin::slip = 2 , ryujin::no_slip = 3 ,   ryujin::dirichlet = 4 , ryujin::dynamic = 5 , ryujin::dirichlet_momentum = 6 }
enum class	ryujin::Ansatz { ryujin::Ansatz::cg_q1 , ryujin::Ansatz::cg_q2 , ryujin::Ansatz::cg_q3 }

Functions
template<int dim, int spacedim, template< int, int > class Triangulation>
void	ryujin::GridGenerator::annulus (Triangulation< dim, spacedim > &, const double, const double, const double, const double)
template<int dim, int spacedim, template< int, int > class Triangulation>
void	ryujin::GridGenerator::cylinder (Triangulation< dim, spacedim > &, const double, const double, const double, const double)
template<int dim, typename T >
void	ryujin::Geometries::populate_geometry_list (T &geometry_list, const std::string &subsection)
template<int dim, template< int, int > class Triangulation>
void	ryujin::GridGenerator::step (Triangulation< dim, dim > &, const double, const double, const double, const double)
template<int dim, int spacedim, template< int, int > class Triangulation>
void	ryujin::GridGenerator::wavetank (Triangulation< dim, spacedim > &, const double, const double, const double, const double)
template<int dim, int spacedim, template< int, int > class Triangulation>
void	ryujin::GridGenerator::wall (Triangulation< dim, spacedim > &, const double, const double, const double)

Detailed Description

Several classes and helper functions for creating meshes for a number of benchmark configurations and controlling the finite element discretization.

Enumeration Type Documentation

Boundary

enum ryujin::Boundary : dealii::types::boundary_id

An enum of type dealii::types::boundary_id that provides an mnemonic for prescribing different boundary conditions on faces.

Note

In deal.II boundary ids are prescribed on faces. However, in our stencil-based method we need such an information for individual boundary degrees of freedom. Thus, the face boundary indicator has to be translated to individual degrees of freedom which happens in OfflineData::prepare() when constructing the OfflineData::boundary_map_ object.

OfflineData::boundary_map_ is a std::multimap that stores all encountered boundary conditions for an individual degree of freedom. The individual algebraic constraint is applied in no particular order. It is thus important to ensure that neighboring boundary conditions, are compatible. For example, inflow conditions prescribed via a Boundary::dirichlet face neighboring a Boundary::no_slip face have to ensure that they prescribe a state compatible with the no slip condition, etc.

Enumerator
do_nothing	The "do nothing" outflow boundary condition: no special treatment of the boundary degree of freedom. For stability reasons it is important to ensure that this boundary id is only prescribed on degrees of freedom with a velocity vector pointing outward of the computational domain and coming from the interior of the domain.
periodic	Prescribe periodic boundary conditions by identifying opposing degrees of freedom. This currently requires a mesh with "standard orientation".
slip	On (free) slip boundary degrees of freedom we enforce a vanishing normal component of the momentum in the Euler module. This is done by explicitly removing the normal component of the momentum for the degree of freedom at the end of TimeStep::euler_step(). In the dissipation module \(v\cdot n\) is enforced strongly which leads to a natural boundary condition on the symmetric stress tensor: \(\tau\cdot\mathbb{S}(v)\cdot\vec n\).
no_slip	On no-slip boundary degrees of freedom we enforce a vanishing normal component of the momentum in the Euler module. This is done by explicitly removing the normal component of the momentum for the degree of freedom at the end of TimeStep::euler_step(). In the dissipation module a vanishing velocity \(v=0\) is enforced strongly.
dirichlet	On degrees of freedom marked as Dirichlet boundary we reset the state of the degree of freedom to the value of InitialData::initial_state(). Such Dirichlet conditions can only be meaningfully enforced as inflow conditions, i.e., the velocity vector associated with a Dirichlet boundary degree of freedom has to point into the computational domain, and no "backward traveling" shock front or other flow feature must reach a Dirichlet boundary degree of freedom during the computation.
dynamic	On degrees of freedom marked as a "dynamic" Dirichlet boundary we reset the state of the degree of freedom to the value of InitialData::initial_state() if the state of the degree of freedom is inflow. Otherwise we do nothing.
dirichlet_momentum	For the Shallow Water Equations: On degrees of freedom marked as "dirichlet momentum" boundary, we reset only the momentum of the degree of freedom to the value of InitialData::initial_state(). Such conditions are used in many steady state problems with inflow conditions.

Definition at line 48 of file discretization.h.

Ansatz

enum class ryujin::Ansatz

strong

An enum class for setting the finite element ansatz.

Enumerator
cg_q1	cG Q1: continuous bi- (tri-) linear Lagrange elements
cg_q2	cG Q2: continuous bi- (tri-) quadratic Lagrange elements
cg_q3	cG Q3: continuous bi- (tri-) cubic Lagrange elements

Definition at line 122 of file discretization.h.

Function Documentation

annulus()

template<int dim, int spacedim, template< int, int > class Triangulation>

void ryujin::GridGenerator::annulus	(	Triangulation< dim, spacedim > &	,
		const double	,
		const double	,
		const double	,
		const double
	)

Create a 2D/3D partial annulus configuration with the given length, height, radii and angle coverage.

We set slip boundary conditions on all boundaries.

Definition at line 23 of file geometry_annulus.h.

Referenced by ryujin::Geometries::Annulus< dim >::create_triangulation().

cylinder()

template<int dim, int spacedim, template< int, int > class Triangulation>

void ryujin::GridGenerator::cylinder	(	Triangulation< dim, spacedim > &	,
		const double	,
		const double	,
		const double	,
		const double
	)

Create a 2D/3D cylinder configuration with the given length and height.

We set Dirichlet boundary conditions on the left boundary and do-nothing boundary conditions on the right boundary. All other boundaries (including the cylinder) have slip boundary conditions prescribed.

The 3D mesh is created by extruding the 2D mesh with a width equal to the "height".

Definition at line 29 of file geometry_cylinder.h.

Referenced by ryujin::Geometries::Cylinder< dim >::create_triangulation().

populate_geometry_list()

template<int dim, typename T >

void ryujin::Geometries::populate_geometry_list	(	T &	geometry_list,
		const std::string &	subsection
	)

Populate a given container with all initial state defined in this namespace

Definition at line 33 of file geometry_library.h.

References ryujin::add().

step()

template<int dim, template< int, int > class Triangulation>

void ryujin::GridGenerator::step	(	Triangulation< dim, dim > &	,
		const double	,
		const double	,
		const double	,
		const double
	)

Create the 2D mach step triangulation.

Even though this function has a template parameter dim, it is only implemented for dimension 2.

Definition at line 23 of file geometry_step.h.

Referenced by ryujin::Geometries::Step< dim >::create_triangulation().

wavetank()

template<int dim, int spacedim, template< int, int > class Triangulation>

void ryujin::GridGenerator::wavetank	(	Triangulation< dim, spacedim > &	,
		const double	,
		const double	,
		const double	,
		const double
	)

Create a 2D numerical wave tank with specifications outlined in Figure 4 of [2018-SW-exps]. The tank consists of a rectangular water reservoir with a long flume attached to the "center" of the reservoir. For the sake of simplicity, we assume the centerline of the flume and reservoir align at y = 0.

All outer walls have "slip" boundary conditions except outer wall at the end of the tank which has dynamic outflow conditions.

Definition at line 28 of file geometry_tank.h.

Referenced by ryujin::Geometries::WaveTank< dim >::create_triangulation().

wall()

template<int dim, int spacedim, template< int, int > class Triangulation>

void ryujin::GridGenerator::wall	(	Triangulation< dim, spacedim > &	,
		const double	,
		const double	,
		const double
	)

Create a 2D double-mach reflection wall configuration:

A rectangular domain with given length and height. The boundary conditions are dirichlet conditions on the top and left of the domain and do-nothing on the right side and the front part of the bottom side from [0, wall_position). Slip boundary conditions are enforced on the bottom side on [wall_position, length).

Definition at line 27 of file geometry_wall.h.

Referenced by ryujin::Geometries::Wall< dim >::create_triangulation().