RinglebMeshGenerator

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 $var element = document.getElementById("moose-equation-3b9d9dd6-9fb2-4ff1-85df-3a5256ed9e22");katex.render("\\gamma = 1.4", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ .

Geometry

Let $var element = document.getElementById("moose-equation-4af8dc10-7afa-4717-abf8-6aa07b17799f");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ be a streamline parameter, i.e., $var element = document.getElementById("moose-equation-936549c9-ab90-4e5c-8c6b-fc12182d69f6");katex.render("k = constant", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ on each streamline. The two stream lines for the two wall boundaries are $var element = document.getElementById("moose-equation-93d1979a-5b22-4c40-87cc-605426b28eae");katex.render("k=k_{max}=1.5", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ for the inner wall, and $var element = document.getElementById("moose-equation-3eb5acea-1723-427e-abd7-3443e69df11a");katex.render("k=k_{min}=0.7", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ for the outer wall. Let $var element = document.getElementById("moose-equation-a205e6cd-17b1-44db-a77b-f69a8d593e4c");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ be the velocity magnitude. For each fixed $var element = document.getElementById("moose-equation-47d971d1-ddba-4df6-bd34-6a5c6e959646");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , $var element = document.getElementById("moose-equation-fbe41e75-6ec9-4c7d-8fac-5bcc702f19f0");katex.render("k_{min} \\leq k \\leq k_{max}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , the variable $var element = document.getElementById("moose-equation-65e43acc-88c7-4ae6-b26a-fa50da26cd9f");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ varies between $var element = document.getElementById("moose-equation-9644d022-e30b-4d62-9aaf-5a72fd218d8a");katex.render("Q_0=0.5", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-2246adf6-2f36-4bfc-8742-3917f5b5c44b");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . For each $var element = document.getElementById("moose-equation-04def252-2e2d-4188-89e3-bf121f490e2a");katex.render("q", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , define the speed of sound $var element = document.getElementById("moose-equation-9aa4f4b2-5215-4c5d-9db3-87b3bb7da8d2");katex.render("a", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , density $var element = document.getElementById("moose-equation-237b348d-2351-4fdc-86a7-72e67d79ebe6");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , pressure $var element = document.getElementById("moose-equation-c075e334-7faf-436e-a140-5374c450967d");katex.render("p", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , and a quantity denoted by $var element = document.getElementById("moose-equation-e9e2e7a2-0956-42fb-bada-b1b50bbf549c");katex.render("J", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ by: $var element = document.getElementById("moose-equation-2eaa39bf-26d2-4da6-b26a-b06503ca2473");katex.render("a=\\sqrt{1 - \\frac{\\gamma-1}{2}q^2};\\quad \\rho = a^{\\frac{2}{\\gamma-1}};\\quad p = \\frac{1}{\\gamma}a^{\\frac{2 \\gamma}{\\gamma-1}};\\quad J = \\frac{1}{a} + \\frac{1}{3a^3} + \\frac{1}{5a^5} - \\frac{1}{2}\\log \\frac{1+a}{1-a}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

For each pair $var element = document.getElementById("moose-equation-e8da9cc3-cb83-40ce-915a-ffbbe09de3b2");katex.render("(q,k)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ , set: $var element = document.getElementById("moose-equation-c610370a-686d-4860-a9f9-9cc83357dcc0");katex.render("x(q,k) = \\frac{1}{2\\rho}\\left( \\frac{2}{k^2}-\\frac{1}{q^2} \\right) - \\frac{J}{2} \\quad \\mathrm{and} \\quad y(q,k) = \\pm \\frac{1}{k \\rho q} \\sqrt{1-\\frac{q^2}{k^2}}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Mesh Overlook

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


[MeshGenerators]
  [./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:

Further RinglebMeshGenerator Documentation

Input Parameters

gammaGamma parameter
C++ Type:double
Options:
Description:Gamma parameter
kmaxValue of k on the inner wall.
C++ Type:double
Options:
Description:Value of k on the inner wall.
kminValue of k on the outer wall.
C++ Type:double
Options:
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
Options:
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
Options:
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
Options:
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
Options:
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
Options:
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
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
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

Optional Parameters

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.

Advanced 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 Overlook
Further RinglebMeshGenerator Documentation
Input Parameters
Input Files

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools