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 $var element = document.getElementById("moose-equation-2088e928-de17-4bea-afeb-4fa6f123fb2e");katex.render("\\gamma = 1.4", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

Geometry

Let $var element = document.getElementById("moose-equation-a870d3e4-af41-4958-b676-dc27fce5ccf9");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ be a streamline parameter, i.e., $var element = document.getElementById("moose-equation-434139ca-b62e-47f5-a961-df877731dcc2");katex.render("k = constant", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ on each streamline. The two stream lines for the two wall boundaries are $var element = document.getElementById("moose-equation-83767d1f-4303-4d43-9dad-a94e9158f8e3");katex.render("k=k_{max}=1.5", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for the inner wall, and $var element = document.getElementById("moose-equation-1da63b87-df72-4926-ac2a-665b6824fd2a");katex.render("k=k_{min}=0.7", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ for the outer wall. Let $var element = document.getElementById("moose-equation-5a5262b5-7686-4ce6-a294-12dd68bc133a");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ be the velocity magnitude. For each fixed $var element = document.getElementById("moose-equation-e6fb2331-1c69-4637-98d1-027169a1dc7d");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-bbdc8f97-0254-4538-84b0-c066542f7012");katex.render("k_{min} \\leq k \\leq k_{max}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the variable $var element = document.getElementById("moose-equation-1ceca162-8f1d-49d5-b552-c1bcd540ad47");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ varies between $var element = document.getElementById("moose-equation-79be0f25-df89-4497-8590-3596290382f9");katex.render("Q_0=0.5", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-ecc2d5e2-af31-419a-bf92-7998ded068c5");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . For each $var element = document.getElementById("moose-equation-d172604d-7934-4ed6-9a84-fe84279f0964");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , define the speed of sound $var element = document.getElementById("moose-equation-1e4ba5d1-a527-49c5-aa20-e0ccef1f7ecb");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , density $var element = document.getElementById("moose-equation-f873b809-c142-4891-a890-d2cf74d3855e");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , pressure $var element = document.getElementById("moose-equation-89379ef8-9978-4c71-a2b5-f3a2ec7bde0b");katex.render("p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and a quantity denoted by $var element = document.getElementById("moose-equation-ee1e1f8e-ece2-4185-a04f-037ff04963c5");katex.render("J", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ by: $var element = document.getElementById("moose-equation-9c32040c-1b1d-44c1-8735-9953b43f7877");katex.render("a=\\sqrt{1 - \\frac{\\gamma-1}{2}q^2};\\quad \\rho = a^{\\frac{2}{\\gamma-1}};\\quad p = \\frac{1}{\\gamma}a^{\\frac{2 \\gamma}{\\gamma-1}};\\quad J = \\frac{1}{a} + \\frac{1}{3a^3} + \\frac{1}{5a^5} - \\frac{1}{2}\\log \\frac{1+a}{1-a}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

For each pair $var element = document.getElementById("moose-equation-c2618414-e5dc-40fd-890f-37221efe7431");katex.render("(q,k)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , set: $var element = document.getElementById("moose-equation-ce67962d-a31a-495a-a7a1-ac4705a3690f");katex.render("x(q,k) = \\frac{1}{2\\rho}\\left( \\frac{2}{k^2}-\\frac{1}{q^2} \\right) - \\frac{J}{2} \\quad \\mathrm{and} \\quad y(q,k) = \\pm \\frac{1}{k \\rho q} \\sqrt{1-\\frac{q^2}{k^2}}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

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
Controllable:No
Description:Gamma parameter
kmaxValue of k on the inner wall.
C++ Type:double
Controllable:No
Description:Value of k on the inner wall.
kminValue of k on the outer wall.
C++ Type:double
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
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
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
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
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
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
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
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
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>
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
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
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
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
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
Controllable:No
Description:Whether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)

Debugging Parameters

Input Files

(test/tests/meshgenerators/ringleb_mesh_generator/ringleb_mesh_generator.i)

(test/tests/meshgenerators/ringleb_mesh_generator/ringleb_mesh_generator.i)

[Mesh]
  [./rmg]
    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
  []
[]

[Outputs]
  exodus = true
[]

Overview
Governing Equations
Geometry
Mesh Example
Input Parameters
Input Files