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 $var element = document.getElementById("moose-equation-7da5ce1e-9736-4ef9-9271-747c390aa07f");katex.render("\\gamma = 1.4", element, {displayMode:false,throwOnError:false});$ .

Geometry

Let $var element = document.getElementById("moose-equation-f3e146c2-5428-40dd-8614-131b4472b7d5");katex.render("k", element, {displayMode:false,throwOnError:false});$ be a streamline parameter, i.e., $var element = document.getElementById("moose-equation-3d5abb7f-7ac5-40a5-9fa1-d449a4361fad");katex.render("k = constant", element, {displayMode:false,throwOnError:false});$ on each streamline. The two stream lines for the two wall boundaries are $var element = document.getElementById("moose-equation-32745d7f-74d2-441e-97a5-7a717d5a0b26");katex.render("k=k_{max}=1.5", element, {displayMode:false,throwOnError:false});$ for the inner wall, and $var element = document.getElementById("moose-equation-d17423e7-8d5e-4073-a566-2d844c7fcbf0");katex.render("k=k_{min}=0.7", element, {displayMode:false,throwOnError:false});$ for the outer wall. Let $var element = document.getElementById("moose-equation-6bb266f1-d2a2-4e94-9ca2-2d71e6dcd1a8");katex.render("q", element, {displayMode:false,throwOnError:false});$ be the velocity magnitude. For each fixed $var element = document.getElementById("moose-equation-01342696-f4df-4095-b2e8-0a4a1b534d3b");katex.render("k", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-a0c51934-1f9a-4579-ac18-86aa28c5f54e");katex.render("k_{min} \\leq k \\leq k_{max}", element, {displayMode:false,throwOnError:false});$ , the variable $var element = document.getElementById("moose-equation-eb2fe202-ae14-4b2c-943d-a1a3d3756dc7");katex.render("q", element, {displayMode:false,throwOnError:false});$ varies between $var element = document.getElementById("moose-equation-93e72060-3842-496c-b50c-5b549e9441e6");katex.render("Q_0=0.5", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-3e73513c-1926-4e01-94e8-bda52851c5ad");katex.render("k", element, {displayMode:false,throwOnError:false});$ . For each $var element = document.getElementById("moose-equation-1e8a9a90-fe30-4533-87ca-0ea45a85ee10");katex.render("q", element, {displayMode:false,throwOnError:false});$ , define the speed of sound $var element = document.getElementById("moose-equation-24c015a2-64ea-4087-9f41-8a68a14c4fd4");katex.render("a", element, {displayMode:false,throwOnError:false});$ , density $var element = document.getElementById("moose-equation-9082e90f-d19a-4a97-80bb-73476a2f9ae1");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ , pressure $var element = document.getElementById("moose-equation-2a5fdd7b-de73-4ea8-a47f-3bb0c17ad4d3");katex.render("p", element, {displayMode:false,throwOnError:false});$ , and a quantity denoted by $var element = document.getElementById("moose-equation-f9e3e2fa-b6da-43fc-8409-69cadc247835");katex.render("J", element, {displayMode:false,throwOnError:false});$ by: $var element = document.getElementById("moose-equation-eb6f20f0-fb4b-46b6-89cf-9cb43ce039c0");katex.render("a=\\sqrt{1 - \\frac{\\gamma-1}{2}q^2};\\quad \\rho = a^{\\frac{2}{\\gamma-1}};\\quad p = \\frac{1}{\\gamma}a^{\\frac{2 \\gamma}{\\gamma-1}};\\quad J = \\frac{1}{a} + \\frac{1}{3a^3} + \\frac{1}{5a^5} - \\frac{1}{2}\\log \\frac{1+a}{1-a}", element, {displayMode:true,throwOnError:false});$

For each pair $var element = document.getElementById("moose-equation-2d831b21-b473-40ec-801a-7f172874f865");katex.render("(q,k)", element, {displayMode:false,throwOnError:false});$ , set: $var element = document.getElementById("moose-equation-e358d2e8-5e82-44d6-9e31-d931791858ec");katex.render("x(q,k) = \\frac{1}{2\\rho}\\left( \\frac{2}{k^2}-\\frac{1}{q^2} \\right) - \\frac{J}{2} \\quad \\mathrm{and} \\quad y(q,k) = \\pm \\frac{1}{k \\rho q} \\sqrt{1-\\frac{q^2}{k^2}}", element, {displayMode:true,throwOnError:false});$

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