GENERATION ALGORITHM - Sandia National LaboratoriesFigure 4: Sweeping for Inlet reactor model 3....
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I MPROVEMENTS TO S WEEPING A SA V OLUME M ESH G ENERATION A LGORITHM { Shengyong Cai and Timothy J. Tautges } CD-adapco, Meshing development, Austin, TX 24th International Meshing Roundtable, Oct 11-14, 2015, Austin, Texas, United States 1. O BJECTIVES The objective is to improve the overall sweep- ing algorithm by improving specific important pieces, demonstrating their impacts in an united implementation. 2. I NTRODUCTION Extrusion of 2D meshes into a general third di- mension is called "sweeping", which consists of four main steps: (a) generate surface meshes over the source surfaces; (b) mapping of source surface meshes onto the target surfaces; (c) generate struc- tured meshes on the linking surfaces; (d) place in- terior nodes inside volumes and generate volume elements. There are three invariants of sweeping from the point of number of s/t surfaces, namely, One-to-One (1-1), Many-to-One (M-1) and Many- to-Many (M-N ). 5. S URFACE M ESH M APPING Harmonic mapping is used to embed s meshes onto t surface: first map both s/t surface faceting onto the common domain and then s meshes are mapped onto t surface through the common do- main. Figure 1: Roadmap of mapping s mesh onto t surface 6. S UBMAPPING Corners during submapping has been assigned based on a combination of templates (fillets, chamfers, rounds and concentric rings) and the optimization approach (guarantee the 4 - 4g submapping constraint). Figure 2: An example of corner assignment R EFERENCES [1] S. Cai and T. J. Tautges. Surface mesh generation based on imprinting of s-t edge patches. Procedia Engineering, 82:325–337, 2014. [2] S. Cai and T. J. Tautges. Robust one-to-one sweeping with harmonic st mappings and cages. Procedings of the 22nd International Meshing Roundtable, pages 1–18, 2013. [3] S. Cai and T. J. Tautges. Optimizing corner assignment of submap surfaces. Procedings of the 24nd International Meshing Roundtable, 2015. F UTURE R ESEARCH • Idealized model creation. • Incorporate geometric constraints in the sweepability problem. • Interior node interpolation on curved sur- faces by submapping. • Parallel meshing: chains of linking surfaces, mesh mapping between s/t surfaces, inte- rior node interpolation inside volumes. 7. I NTERIOR NODE PLACEMENT A global interior node placement algorithm based on cage-based method has been developed, con- sisting of 4 main steps: idealized cage creation, interior node placement inside idealized model, binding of boundary nodes with interior nodes (location of interior nodes is a function of bound- ary surface mesh nodes) and interior node place- ment inside physical models. Figure 3: Pipeline of placing inner nodes 8. E XAMPLES AND C ONCLUSION The overall sweeping algorithm is improved by improving specific important pieces, demon- strated their impacts in an united implementa- tion. Figure 4: Sweeping for Inlet reactor model 3. P IPELINE OF S WEEPING Figure 5: An example of our multi-sweeping pipeline Figure 6: Pipeline of our multi-sweeping approach 4. E DGE P ATCH I MPRINTING An edge patch imprinting based on cage-based morphing for multi-sweeping problems has been developed, which is used to resolve conflicts of vertices and edges between s/t surfaces(embed s vertices/edges onto the t surfaces. This results in: each s surface patch is paired with exactly one t patch after imprinting. mesh and vice versa). Figure 7: Edge patch imprinting between s/t surfaces Figure 8: Crankshaft
Transcript of GENERATION ALGORITHM - Sandia National LaboratoriesFigure 4: Sweeping for Inlet reactor model 3....
IMPROVEMENTS TO SWEEPING AS A VOLUME MESHGENERATION ALGORITHM
{ Shengyong Cai and Timothy J. Tautges } CD-adapco, Meshing development, Austin, TX24th International Meshing Roundtable, Oct 11-14, 2015, Austin, Texas, United States
1. OBJECTIVESThe objective is to improve the overall sweep-ing algorithm by improving specific importantpieces, demonstrating their impacts in an unitedimplementation.
2. INTRODUCTIONExtrusion of 2D meshes into a general third di-mension is called "sweeping", which consists offour main steps: (a) generate surface meshes overthe source surfaces; (b) mapping of source surfacemeshes onto the target surfaces; (c) generate struc-tured meshes on the linking surfaces; (d) place in-terior nodes inside volumes and generate volumeelements. There are three invariants of sweepingfrom the point of number of s/t surfaces, namely,One-to-One (1-1), Many-to-One (M-1) and Many-to-Many (M-N).
5. SURFACE MESH MAPPINGHarmonic mapping is used to embed s meshesonto t surface: first map both s/t surface facetingonto the common domain and then s meshes aremapped onto t surface through the common do-main.
Figure 1: Roadmap of mapping s mesh onto t surface
6. SUBMAPPINGCorners during submapping has been assignedbased on a combination of templates (fillets,chamfers, rounds and concentric rings) and theoptimization approach (guarantee the 4 − 4gsubmapping constraint).
Figure 2: An example of corner assignment
REFERENCES
[1] S. Cai and T. J. Tautges. Surface mesh generation based on imprinting of s-t edge patches. Procedia Engineering,82:325–337, 2014.
[2] S. Cai and T. J. Tautges. Robust one-to-one sweeping with harmonic st mappings and cages. Procedings of the22nd International Meshing Roundtable, pages 1–18, 2013.
[3] S. Cai and T. J. Tautges. Optimizing corner assignment of submap surfaces. Procedings of the 24nd InternationalMeshing Roundtable, 2015.
FUTURE RESEARCH
• Idealized model creation.
• Incorporate geometric constraints in thesweepability problem.
• Interior node interpolation on curved sur-
faces by submapping.
• Parallel meshing: chains of linking surfaces,mesh mapping between s/t surfaces, inte-rior node interpolation inside volumes.
7. INTERIOR NODE PLACEMENTA global interior node placement algorithm basedon cage-based method has been developed, con-sisting of 4 main steps: idealized cage creation,interior node placement inside idealized model,binding of boundary nodes with interior nodes(location of interior nodes is a function of bound-ary surface mesh nodes) and interior node place-ment inside physical models.
Figure 3: Pipeline of placing inner nodes
8. EXAMPLES AND CONCLUSIONThe overall sweeping algorithm is improvedby improving specific important pieces, demon-strated their impacts in an united implementa-tion.
Figure 4: Sweeping for Inlet reactor model
3. PIPELINE OF SWEEPING
Figure 5: An example of our multi-sweeping pipeline
Figure 6: Pipeline of our multi-sweeping approach
4. EDGE PATCH IMPRINTINGAn edge patch imprinting based on cage-basedmorphing for multi-sweeping problems has beendeveloped, which is used to resolve conflicts ofvertices and edges between s/t surfaces(embed svertices/edges onto the t surfaces. This results in:each s surface patch is paired with exactly one tpatch after imprinting. mesh and vice versa).
Figure 7: Edge patch imprinting between s/t surfaces
Figure 8: Crankshaft
