# RinglebMesh

## Overview

This mesh can be applied to a Ringleb problem. This problem tests the spatial accuracy of high-order methods. The flow is transonic and smooth. The geometry is also smooth, and high-order curved boundary representation appears to be critical.

## Governing Equations

The governing equations are the 2D Euler equations with .

## Geometry

Let be a streamline parameter, i.e., on each streamline. The two stream lines for the two wall boundaries are for the inner wall, and for the outer wall. Let be the velocity magnitude. For each fixed , , the variable varies between and . For each , define the speed of sound , density , pressure , and a quantity denoted by by:

For each pair , set:

## Mesh Overlook

For example, let's consider the following input file:


[Mesh]
type = RinglebMesh
kmin = 0.7
num_k_pts = 9
num_q_pts = 20
kmax = 1.2
n_extra_q_pts = 2
gamma = 1.4
triangles = true
[]


The corresponding mesh looks like this:

## Input Parameters

• num_k_ptsHow many points in the range k=(kmin, kmax).

C++ Type:int

Options:

Description:How many points in the range k=(kmin, kmax).

• kminValue of k on the outer wall.

C++ Type:double

Options:

Description:Value of k on the outer wall.

• num_q_ptsHow many points to discretize the range q = (0.5, k) into.

C++ Type:int

Options:

Description:How many points to discretize the range q = (0.5, k) into.

• n_extra_q_ptsHow many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.

C++ Type:int

Options:

Description:How many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.

• kmaxValue of k on the inner wall.

C++ Type:double

Options:

Description:Value of k on the inner wall.

• gammaGamma parameter

C++ Type:double

Options:

Description:Gamma parameter

### Required Parameters

• outer_wall_bid4The boundary id to use for the outer wall

Default:4

C++ Type:short

Options:

Description:The boundary id to use for the outer wall

• outflow_bid3The boundary id to use for the outflow

Default:3

C++ Type:short

Options:

Description:The boundary id to use for the outflow

• allow_renumberingTrueIf allow_renumbering=false, node and element numbers are kept fixed until deletion

Default:True

C++ Type:bool

Options:

Description:If allow_renumbering=false, node and element numbers are kept fixed until deletion

• ghosting_patch_sizeThe number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.

C++ Type:unsigned int

Options:

Description:The number of nearest neighbors considered for ghosting purposes when 'iteration' patch update strategy is used. Default is 5 * patch_size.

• inner_wall_bid2The boundary id to use for the inner wall

Default:2

C++ Type:short

Options:

Description:The boundary id to use for the inner wall

• inflow_bid1The boundary id to use for the inflow

Default:1

C++ Type:short

Options:

Description:The boundary id to use for the inflow

• max_leaf_size10The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.

Default:10

C++ Type:unsigned int

Options:

Description:The maximum number of points in each leaf of the KDTree used in the nearest neighbor search. As the leaf size becomes larger,KDTree construction becomes faster but the nearest neighbor searchbecomes slower.

• trianglesFalseIf true, all the quadrilateral elements will be split into triangles

Default:False

C++ Type:bool

Options:

Description:If true, all the quadrilateral elements will be split into triangles

• parallel_typeDEFAULTDEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh

Default:DEFAULT

C++ Type:MooseEnum

Options:DEFAULT REPLICATED DISTRIBUTED

Description:DEFAULT: Use libMesh::ReplicatedMesh unless --distributed-mesh is specified on the command line REPLICATED: Always use libMesh::ReplicatedMesh DISTRIBUTED: Always use libMesh::DistributedMesh

### Optional Parameters

• dim1This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!

Default:1

C++ Type:MooseEnum

Options:1 2 3

Description:This is only required for certain mesh formats where the dimension of the mesh cannot be autodetected. In particular you must supply this for GMSH meshes. Note: This is completely ignored for ExodusII meshes!

• nemesisFalseIf nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.

Default:False

C++ Type:bool

Options:

Description:If nemesis=true and file=foo.e, actually reads foo.e.N.0, foo.e.N.1, ... foo.e.N.N-1, where N = # CPUs, with NemesisIO.

• patch_update_strategyneverHow often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all slave nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all slave nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of slave nodes for which penetration is not detected. If there can be substantial relative motion between the master and slave surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.

Default:never

C++ Type:MooseEnum

Options:never always auto iteration

Description:How often to update the geometric search 'patch'. The default is to never update it (which is the most efficient but could be a problem with lots of relative motion). 'always' will update the patch for all slave nodes at the beginning of every timestep which might be time consuming. 'auto' will attempt to determine at the start of which timesteps the patch for all slave nodes needs to be updated automatically.'iteration' updates the patch at every nonlinear iteration for a subset of slave nodes for which penetration is not detected. If there can be substantial relative motion between the master and slave surfaces during the nonlinear iterations within a timestep, it is advisable to use 'iteration' option to ensure accurate contact detection.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• construct_node_list_from_side_listTrueWhether or not to generate nodesets from the sidesets (usually a good idea).

Default:True

C++ Type:bool

Options:

Description:Whether or not to generate nodesets from the sidesets (usually a good idea).

• patch_size40The number of nodes to consider in the NearestNode neighborhood.

Default:40

C++ Type:unsigned int

Options:

Description:The number of nodes to consider in the NearestNode neighborhood.

• partitionerdefaultSpecifies a mesh partitioner to use when splitting the mesh for a parallel computation.

Default:default

C++ Type:MooseEnum

Options:default metis parmetis linear centroid hilbert_sfc morton_sfc

Description:Specifies a mesh partitioner to use when splitting the mesh for a parallel computation.

• centroid_partitioner_directionSpecifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial

C++ Type:MooseEnum

Options:x y z radial

Description:Specifies the sort direction if using the centroid partitioner. Available options: x, y, z, radial