尺寸函数sizing-function

Tutorial:Introduction to Size FunctionsPurposeThe purpose of this tutorial is to introduce you to the use of size functions to control the size of mesh intervals for edges and mesh elements for faces and volumes.Based on their application,there are four types of size functions:fixed,curvature,proximity and meshed.This tutorial shows you how to use these size function types to refine a mesh in regions surrounding a specified entity and how to combine boundary layers and size functions for better mesh quality.PrerequisitesThis tutorial assumes that you are familiar with the GAMBIT interface and have a basic understanding of geometry creation and size functions.If you have not used size functions before,you can refer to Section5.2:Size Functions,in the GAMBIT Modeling Guide(http://www.fl/gambit2/doc/doc f.htm).Problem DescriptionYou will create a rectangular face,an elliptical cylindrical volume and a brick geometry and mesh them using the Fixed,Curvature,and Proximity size functions,respectively.Using a journalfile,you will then create and partially premesh2-D and3-D geometry.You will then use the meshed size function to grow the full mesh from the premeshed sections of the geometry.To create a size function,you need to define the Source and Attachment entities and param-eters such as,Growth rate,Size limit,Start size,Angle,and Cells/gap.The Growth rate and Size limit parameters are common to the four size functions.The additional parameter specific to three size functions,which is the initialization parameter used to create mesh on the source entities,is listed below:Type of Size Function Parameter Specific to the FunctionFixed Start sizeCurvature AngleProximity Cells/gapThe meshed size function does not require an initialization parameter,since we are starting from an existing mesh at the source entities.Introduction to Size FunctionsYou can specify more than one size function on any face or volume.Size functions can be used with hexahedral,tetrahedral or hybrid volume meshes and quadilateral or triangular face meshes.Since,you can control the number of elements in mapped or submapped meshes using edge grading,size functions are used in more complex geometries where tetrahedral or Cooper meshing schemes are required.Fixed Size FunctionThe Fixed size function is used to control the maximum mesh-element edge lengths in a model.Step1:Geometry1.Start GAMBIT with the identifier pipe.2.Create a rectangle with the following dimensions:Width Height10103.Create a circle with a value of Radius as1.4.Subtract the circle from the square.(a)In the Subtract Real Faces form,select face.1and face.2for Face and Subtract Facesrespectively.(b)Retain the default values of the other parameters and click Apply.5.Make two copies of the face and translate it.(a)In the Move/Copy Faces form,select face.1for Faces.(b)Select Copy and set the number of copies to2.(c)Under Global,set the value of x:to12.(d)Retain the default values of the other parameters and click Apply.Step2:Mesh the First Face1.Mesh the inner circular loop on thefirst face.(a)In the Mesh Edges form,for Edges,select the edge corresponding to the innercircular loop.(b)Set the Interval size to0.2and click Apply.2.Mesh thefirst face(see Figure1).(a)In the Mesh Faces form,select face.1for Faces and Tri for Elements:.(b)Retain the default values for the other parameters and click Apply.Introduction to Size FunctionsFigure1:Mesh on face.1Step3:Mesh the Second Face Using the Fixed Size Function1.Define afixed type function(fix1)on the second face(face.2).(a)On the Entities:Source:option button,select Edges and select the edge corre-sponding to the inner circular loop.(b)On the Entities:Attachment:option button,select the second face(face.2).(c)Set the values for the remaining parameters as follows:Start size Growth rate Size limit Label0.2 1.50.5fix12.Initialize the size function.(a)In the View Size Function form,selectfix1for S.Function and click Initialize.Note:The Iso-value:ranges from0.2to0.5.You can move the slider bar to examine the extent of the size function.The size function will not encompass the entireface.In the region excluded by the isovalues from0.2to0.5,the elements willhave a constant size of0.5.3.Mesh the second face.(a)Select face.2for Faces and Tri for Elements:.(b)Click Apply.The mesh obtained is muchfiner than the mesh on thefirst face because the valueof Size limit was specified as0.5.Introduction to Size Functions4.Delete the mesh on the second face.You will now adjust the size function parameters to get a coarser mesh on the secondface.5.Modify the size function(fix1)on the second face.(a)Change the value of Size limit to1and retain the default values of the otherparameters.6.Reinitialize the size function.Note:The Iso-value:now ranges from0.2to1.You can move the slider bar to examine the extent of the size function.The size function will not encompass theentire face.In the region excluded by the isovalues from0.2to1,the elementswill have a constant size of1.7.Remesh the second face(see Figure2).With the modified size function,you get a coarser mesh on the second face.Figure2:Mesh on face.2Step4:Mesh the Third Face Using the Fixed Size Function1.Define afixed type function(fix2)on the third face.(a)Set the Source:to the edge corresponding to the inner circular loop.(b)Set the Attachment:to face.3.(c)Set the values for the remaining parameters as follows:Start size Growth rate Size limit Label0.2 1.21fix2Introduction to Size Functions2.Initialize the size function.(a)In the View Size Function form,selectfix2for S.Function and click Initialize.Note:The Iso-value:ranges from0.2to1.You can move the slider bar to examine the extent of the size function.The size function will encompass the entire face.In the region excluded by the isovalues from0.2to1,the elements will have aconstant size of1.3.Mesh the third face with Tri elements.Figure3:Mesh on face.3You can compare the meshes shown in Figures1,2,and3.All the three meshes have the same mesh sizes on the edges,but the meshes created using a size function have a prescribed growth rate that results in fewer elements.Introduction to Size FunctionsCurvature Size FunctionThe Curvature size function controls the angles between the normals for adjacent mesh ele-ments and is useful when the model contains highly curved surfaces.Step1:Geometry1.Delete the previously created faces(face.1,face.2,and face.3).2.Create an elliptical cylinder with the following parameters:Height Radius1Radius2Axis Location1025Centered Z3.Make two copies of the elliptical cylinder and translate them.(a)In the Move/Copy Volumes form,select volume.1for Volumes and set the numberof copies to2.(b)Under Global,set the value of y:to12and x:and z:to0.(c)Retain the default values of the other parameters and click Apply.Step2:Mesh the First Volume1.In the Mesh Volumes form,select volume.1for Volumes and Tet/Hybrid for Elements:.2.Set the Interval size to2and click Apply.Figure4:Mesh on volume.1The mesh poorly represents the model in the regions where the edges are highly curvedand the surfaces are non planar.Introduction to Size Functions Step3:Mesh the Second Volume Using the Curvature Size Function1.Define a curvature type function(curv1).(a)Select Curvature for Type:.(b)On the Entities:Source:option button,select Faces and select the lateral face ofvolume.2.(c)On the Entities:Attachment:option button,select Volumes and select the volumeas volume.2.(d)Set the values for the remaining parameters as follows:Angle Growth rate Size limit Label40 1.22curv12.Mesh the second volume(volume.2)using tetrahedral elements.Figure5:Mesh on volume.2Now,the mesh is a much better approximation of the model where the regions are highly curved.Introduction to Size FunctionsStep4:Mesh the Third Volume Using the Curvature Size Function1.Define a curvature type function(curv2)on the third volume(volume.3).(a)Set the Source:to the lateral face of volume.3and the Attachment:to volume.3.(b)Change the value of Angle to20,and refer to the definition of curv1for values ofthe other parameters.2.Mesh the third volume(volume.3)using tetrahedral elements.Figure6:Mesh on volume.3pare the meshes for the second and third volume(see Figure7).The value of the angle determines the maximum angle between the normal vectors to adjacent mesh elements.Thus,a smaller angle(20degrees)will produce a better approximation toa curved edge than a larger angle(40degrees).Introduction to Size FunctionsFigure7:Magnified View of the Curved Edges of volume.3and volume.2Introduction to Size FunctionsProximity Size FunctionThe Proximity size function controls the number of mesh elements in faces between two geometric entities and is useful when there are small gaps in the model.Step1:Geometry1.Delete the previously created volumes(volume.1,volume.2and volume.3).2.Create a brick with the following dimensions:Width Depth Height Direction555Centered3.Create a thinner brick with the following dimensions:Width Depth Height Direction0.255Centered4.Move the thinner brick.(a)In the Move/Copy Volumes form,select volume.2or Volumes,and under Global,setthe values of x:to2,y:to0,and z:to2.5.5.Subtract the thinner brick from the larger brick.(a)In the Subtract Real Volumes form,select volume.1for Volume and volume.2forSubtract Volumes and click Apply.Figure8:Subtracted Volume(volume.1)There is a thin rectangular face(face.11)and a small gap of0.4width within thevolume bounded by the faces,face.13and face.1.6.Make a copy of the volume and translate it.(a)In the Move/Copy Volumes form,select volume.1for Volumes and set the numberof copies to1.(b)Under Global,set the value of x:to6,and y:and z:to0.(c)Retain the default values of the other parameters and click Apply.Step2:Mesh the First Volume Using Proximity Size Function1.Define a proximity type function(prox1)on thefirst volume(volume.1).(a)Select Proximity for Type:.(b)On the Entities:Source:option button,select Faces and select the thin rectangularface(face.11)of volume.1.(c)On the Entities:Attachment:option button,select Volumes and select the volumeas volume.1.(d)Set the values for the remaining parameters as follows:Cells/gap Growth rate Size limit Label3 1.31prox12.Mesh volume.1using tetrahedral elements.Figure9:Mesh on volume.1Figure10:Magnified View of Mesh on volume.1There are3elements in the thin rectangular face(face.11),however there is only one element in the thin gap bounded by the faces,face.13and face.1.Step3:Mesh the Second Volume Using Proximity Size Function1.Define a proximity function(prox2)on the second volume.(a)Set the Source:to the three faces(face.17,face.16,and face.25)of volume.2.(b)Set the Attachment:to volume.2,and refer to the definition of prox1for values ofthe other parameters.2.Mesh volume.2using tetrahedral elements.Now,there are3elements in the thin rectangular face(face.17)and three elements in the thin gap bounded by the faces,face.16,and face.25(see Figure12).Figure11:Mesh on volume.2Figure12:Magnified View of Mesh on volume.2Meshed Size FunctionThe meshed size function is used to grow mesh from source entities,which have been premeshed.This size function can be used for growing a graded surface mesh from pre-meshed edges or graded volume meshes from premeshed faces.You will need the journal file,meshed-sf-prep.jou for this section.Step1:Geometry and Premeshing using a Journal File1.Start GAMBIT with the identifier meshed-sf.2.In the File menu,select Run Journal....3.In the Run Journal form,select the Edit/Run mode.4.Click Browse...and navigate to the directory containing the journalfile meshed-sf-prep.jou.5.Select thefile meshed-sf-prep.jou and click Accept.6.In the Edit/Run Journal form,right-click the mouse and choose Select All in the drop-down menu.7.Click Step repeatedly to execute the commands in the journalfile one after another. Note:Observe the sequence of events on the screen from geometry creation to meshing ofedges and face.You may need to click the button to view all geometry.Step2:Mesh the First Face Using a Meshed Size Function1.Create a meshed size function with source as the edges and attachment entity asface.1.(a)Select Meshed as Type:.(b)On the Entities:Source:option button,select Edges and select all four premeshededges of thefirst face.(c)On the Entities:Attachment:option button,select thefirst face(face.1).(d)Set the values of the parameters as follows:Growth Rate Size Limit Label1.12meshed12.Mesh the face with quadrilaterals using the quad pave scheme.Figure13:Face Meshed Using Quad Pave SchemeIt can be observed that the mesh grows into the face from the edge meshes(Figure13).The face mesh can be made smoother orfiner by adjusting the growth rate and the size limit.This is useful for meshing complex faces containing edge meshes with different grading and spacing.Step3:Mesh the Volume Using a Meshed Size Function3.Create a meshed size function with source as the meshed face and attachment entityas volume.(a)Select Meshed as Type:.(b)On the Entities:Source:option button,select the Faces and select the premeshedface of the volume.(c)On the Entities:Attachment:option button,select Volume and select the volume(volume.1).(d)Set the values of the parameters as follows:Growth Rate Size Limit Label1.24meshed24.Mesh the volume with a Tet/Hybrid mesh using the Tgrid meshing scheme.Figure14:Cross-Sectional View of Mesh Along Length of the Volume It can be observed that the mesh grows from the premeshed face into the volume(Fig-ure14).The mesh can be changed by changing the growth rate and the size limit.This is useful in ensuring a smooth transition in mesh between different sections of a larger geometry or in growing a volume mesh from premeshed complex surfaces.In addition, the meshed sizing function can be used for creating a volume mesh grown from the end-capping surface of a prismatic boundary layer grown from surface meshes.Combining the Size Function and Boundary LayerSizing functions can also be combined with boundary layers.In the following example,the volume contains an interior void and the boundary layer must be attached to all the interior faces of this void.In this case,the internal continuity must be turned on.Step1:Geometry1.Delete the previously created volumes(volume.1and volume.2).2.Create a brick with the following dimensions:Width Depth Height Direction141414Centered3.Create an elliptical cylinder with the following parameters:Height Radius1Radius2Axis Location513Centered Z4.Subtract the cylinder from the brick.5.Make two copies of the subtracted volume and translate it.(a)Under Global,set the value of x:to16and y:and z:to0.Step2:Mesh the First Volume Using Size Functions1.Define a curvature type function curvbl1on thefirst volume(volume.1).(a)Select Curvature for Type:.(b)On the Entities:Source:option button,select Faces and select the lateral face ofthe cylinder.(c)On the Entities:Attachment:option button,select Volumes and select the volumeas volume.1.(d)Set the values for the remaining parameters as follows:Angle Growth rate Size limit Label30 1.31curvbl12.Mesh the volume using tetrahedral elements.3.Examine the mesh(see Figure15).(a)Set the Display Type:to Plane and select the tetrahedral3D Element.Figure15:Slice of the Mesh in the z directionStep3:Mesh the Second Volume Using Size Functions and Boundary Layer1.Define a curvature type function(curvbl2)on the second volume using the definitionfor curvbl1.2.Create a boundary layer for volume.2using the Uniform algorithm.(a)Set the values of the following parameters:First row Growth factor Rows0.2 1.23(b)Turn on Internal continuity.(c)Define the three faces(face.16,face.17,and face.18)of the cylinder as the At-tachment:.(d)Retain the default values for the other parameters and click Apply.3.Mesh the volume using tetrahedral elements.4.Examine the mesh.(a)Set the Display Type:to Plane and select the wedge3D Element.(b)Slide the slider bar in the Z direction(see Figure16).As you have used the uniform based boundary layer,you will see that the heightof thefirst layer of prism elements is constant.Figure16:Magnified View of the Prism Elements in the Boundary Layer(c)Select the tetrahedral3D Element and examine the growth of the elements out-wards from the interior void(see Figure17).Figure17:Slice of the mesh in the z directionStep4:Mesh the Third Volume Using Size Functions and Boundary Layer1.Define a curvature type function(curvbl3)on the third volume using the definition forcurvbl1.2.Create a boundary layer for volume.3using the Aspect ratio based algorithm.(a)Set the values of the following parameters:First percent Growth factor Rows30 1.23(b)Turn on Internal continuity.(c)Define the three faces(face.25,face.26,and face.27)of the cylinder as the At-tachment:.3.Mesh the volume using tetrahedral elements.4.Examine the mesh.(a)Set the Display Type:to Plane and select the wedge3D Element.(b)Slide the slider bar in the Z direction(see Figure18).Figure18:Magnified View of the Prism Elements in the Boundary LayerAs you have used the aspect ratio based boundary layer,you will see that theheight of thefirst layer of prism elements is not constant.Introduction to Size Functions(c)Select the tetrahedral3D Element and examine the growth of the elements out-wards from the interior void(see Figure19).Figure19:Slice of the Mesh in the z directionc Fluent Inc.June3,200521。