RinglebMeshGenerator

Creates a mesh for the Ringleb problem.

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 $var element = document.getElementById("moose-equation-4f3d29ba-7489-4c88-9682-43c032b15bfd");katex.render("\\gamma = 1.4", element, {displayMode:false,throwOnError:false});$ .

Geometry

Let $var element = document.getElementById("moose-equation-e9319481-ccd9-4423-89d6-f081f1c09791");katex.render("k", element, {displayMode:false,throwOnError:false});$ be a streamline parameter, i.e., $var element = document.getElementById("moose-equation-80900a34-255a-4e50-8d8a-e10a60e5002c");katex.render("k = constant", element, {displayMode:false,throwOnError:false});$ on each streamline. The two stream lines for the two wall boundaries are $var element = document.getElementById("moose-equation-4dc6ee41-d985-4d2e-8ffb-399b8ccfe596");katex.render("k=k_{max}=1.5", element, {displayMode:false,throwOnError:false});$ for the inner wall, and $var element = document.getElementById("moose-equation-fc84841d-b789-4460-9076-9853b466d091");katex.render("k=k_{min}=0.7", element, {displayMode:false,throwOnError:false});$ for the outer wall. Let $var element = document.getElementById("moose-equation-6d471136-bfe0-43e9-9206-262ebdf339c5");katex.render("q", element, {displayMode:false,throwOnError:false});$ be the velocity magnitude. For each fixed $var element = document.getElementById("moose-equation-a2f5ef18-51f3-45c9-b863-401744fcdc50");katex.render("k", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-e76e94d3-617c-4f88-9256-4e4d82cafb39");katex.render("k_{min} \\leq k \\leq k_{max}", element, {displayMode:false,throwOnError:false});$ , the variable $var element = document.getElementById("moose-equation-e3f82e73-1d8a-4e44-a768-8feb9049369d");katex.render("q", element, {displayMode:false,throwOnError:false});$ varies between $var element = document.getElementById("moose-equation-58c88874-ecc7-4631-bde6-3367904bc3f3");katex.render("Q_0=0.5", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-7f1c3599-dd20-4c12-a15f-1644993e225f");katex.render("k", element, {displayMode:false,throwOnError:false});$ . For each $var element = document.getElementById("moose-equation-17645029-fa87-4ece-b95c-cb828aca3435");katex.render("q", element, {displayMode:false,throwOnError:false});$ , define the speed of sound $var element = document.getElementById("moose-equation-7b9a87dd-45f3-4215-90f5-f1c1ea1c189b");katex.render("a", element, {displayMode:false,throwOnError:false});$ , density $var element = document.getElementById("moose-equation-09c44170-a50b-424e-8190-62ba4ab44f20");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ , pressure $var element = document.getElementById("moose-equation-9624b5f6-f6ff-444b-9800-3f26c604afd0");katex.render("p", element, {displayMode:false,throwOnError:false});$ , and a quantity denoted by $var element = document.getElementById("moose-equation-e3cf2f48-4232-4d80-9ab9-a5a572255186");katex.render("J", element, {displayMode:false,throwOnError:false});$ by: $var element = document.getElementById("moose-equation-0861dea7-4a3a-4c94-8588-aa983f06cf26");katex.render("a=\\sqrt{1 - \\frac{\\gamma-1}{2}q^2};\\quad \\rho = a^{\\frac{2}{\\gamma-1}};\\quad p = \\frac{1}{\\gamma}a^{\\frac{2 \\gamma}{\\gamma-1}};\\quad J = \\frac{1}{a} + \\frac{1}{3a^3} + \\frac{1}{5a^5} - \\frac{1}{2}\\log \\frac{1+a}{1-a}", element, {displayMode:true,throwOnError:false});$

For each pair $var element = document.getElementById("moose-equation-002a5867-89cb-4141-8a6e-ac20b00853c6");katex.render("(q,k)", element, {displayMode:false,throwOnError:false});$ , set: $var element = document.getElementById("moose-equation-cddbc390-2cdc-4890-9e32-02fe2a396c11");katex.render("x(q,k) = \\frac{1}{2\\rho}\\left( \\frac{2}{k^2}-\\frac{1}{q^2} \\right) - \\frac{J}{2} \\quad \\mathrm{and} \\quad y(q,k) = \\pm \\frac{1}{k \\rho q} \\sqrt{1-\\frac{q^2}{k^2}}", element, {displayMode:true,throwOnError:false});$

Mesh Example

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


[Mesh]
  [./ringleb]
    type = RinglebMeshGenerator
    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

gammaGamma parameter
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Gamma parameter
kmaxValue of k on the inner wall.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value of k on the inner wall.
kminValue of k on the outer wall.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value of k on the outer wall.
n_extra_q_ptsHow many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:How many 'extra' points should be inserted in the final element *in addition to* the equispaced q points.
num_k_ptsHow many points in the range k=(kmin, kmax).
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:How many points in the range k=(kmin, kmax).
num_q_ptsHow many points to discretize the range q = (0.5, k) into.
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:How many points to discretize the range q = (0.5, k) into.

Required Parameters

inflow_bid1The boundary id to use for the inflow
Default:1
C++ Type:short
Unit:(no unit assumed)
Controllable:No
Description:The boundary id to use for the inflow
inner_wall_bid2The boundary id to use for the inner wall
Default:2
C++ Type:short
Unit:(no unit assumed)
Controllable:No
Description:The boundary id to use for the inner wall
outer_wall_bid4The boundary id to use for the outer wall
Default:4
C++ Type:short
Unit:(no unit assumed)
Controllable:No
Description:The boundary id to use for the outer wall
outflow_bid3The boundary id to use for the outflow
Default:3
C++ Type:short
Unit:(no unit assumed)
Controllable:No
Description:The boundary id to use for the outflow
trianglesFalseIf true, all the quadrilateral elements will be split into triangles
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:If true, all the quadrilateral elements will be split into triangles

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.
save_with_nameKeep the mesh from this mesh generator in memory with the name specified
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Keep the mesh from this mesh generator in memory with the name specified

Advanced Parameters

nemesisFalseWhether or not to output the mesh file in the nemesisformat (only if output = true)
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to output the mesh file in the nemesisformat (only if output = true)
outputFalseWhether or not to output the mesh file after generating the mesh
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to output the mesh file after generating the mesh
show_infoFalseWhether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Whether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)

Debugging Parameters

Overview
Governing Equations
Geometry
Mesh Example
Input Parameters