On the use of characteristic-based split meshfree method for solving flow problems
This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new f...
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| Published in | International journal for numerical methods in fluids Vol. 56; no. 10; pp. 1885 - 1907 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
10.04.2008
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0271-2091 1097-0363 |
| DOI | 10.1002/fld.1529 |
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| Abstract | This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time‐dependent and steady‐state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. Copyright © 2007 John Wiley & Sons, Ltd. |
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| AbstractList | This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time‐dependent and steady‐state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. Copyright © 2007 John Wiley & Sons, Ltd. This study presents characteristic-based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was initially introduced in finite element framework. In this work, the general equations of flow have been represented in the meshfree context. A new finite element and MFree code is developed for solving flow problems. This computational code is capable of solving both time-dependent and steady-state flow problems. Numerical simulation of some known benchmark flow problems has been studied. Computational results of MFree method have been compared to those of finite element method. The results obtained have been verified by known numerical, analytical and experimental data in the literature. A number of shape functions are used for field variable interpolation. The performance of each interpolation method is discussed. It is concluded that the MFree method is more accurate than FEM if the same numbers of nodes are used for each solver. Meshfree CBS algorithm is completely stable even at high Reynolds numbers. |
| Author | Shamekhi, Abazar Sadeghy, Kayvan |
| Author_xml | – sequence: 1 givenname: Abazar surname: Shamekhi fullname: Shamekhi, Abazar email: ashamekh@ut.ac.ir organization: Faculty of Mechanical Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran – sequence: 2 givenname: Kayvan surname: Sadeghy fullname: Sadeghy, Kayvan organization: Faculty of Mechanical Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran |
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| Cites_doi | 10.1002/(SICI)1097-0363(199706)24:12<1391::AID-FLD566>3.0.CO;2-2 10.1201/9781420040586 10.1007/3-540-36228-2 10.1002/nme.760 10.1090/S0025-5718-1981-0616367-1 10.1080/10407790050051146 10.1002/nme.1620340218 10.1090/S0025-5718-1968-0242392-2 10.1080/10407788208913459 10.1142/S0219876205000491 10.1002/nme.618 10.1007/s004660050402 10.1086/112164 10.1002/(SICI)1097-0207(20000110/30)47:1/3<537::AID-NME783>3.0.CO;2-E 10.1017/S0022112083002839 10.1016/S0955-7997(02)00028-0 10.1002/fld.365 10.1016/S0955-7997(02)00017-6 10.1007/BF00364252 10.1016/0021-9991(82)90058-4 10.1016/S0898-1221(01)00293-0 10.1002/fld.1650200812 10.1093/mnras/181.3.375 10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P 10.1002/fld.1650051104 10.1002/fld.1650200824 |
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| Keywords | meshfree method Pipe flow Eccentricity Computational fluid dynamics Annular space Digital simulation Computation code characteristic-based split algorithm Step Cavity flow fluid dynamics Moving wall Finite element method Algorithms fluid flow Meshless method Modelling Rotating cylinder |
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| References | Zienkiewicz OC, Codina R. A general algorithm for compressible and incompressible flow. Part I. The split characteristic based scheme. International Journal for Numerical Methods in Fluids 1995; 20:869-885. Lucy L. A numerical approach to testing the fission hypotheses. Astronomical Journal 1977; 82:1013-1024. Tsukanov I, Shapiro V, Zhang S. A meshfree method for incompressible fluid dynamics problems. International Journal for Numerical Methods in Engineering 2003; 58:127-158. Ramaswamy B, Jue TC, Akin JE. Semi-implicit and explicit finite element schemes for coupled fluid thermal problems. International Journal for Numerical Methods in Engineering 1992; 34:675-696. Zienkiewicz OC, Taylor RL. The Finite Element Method (4th edn), vol. 1. McGraw-Hill: New York, 1989. Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318. Liu WK, Jun S, Sihling DT, Chen YJ, Hao W. Multiresolution reproducing kernel particle method for computational fluid dynamics. International Journal for Numerical Methods in Fluids 1997; 24(12):1391-1415. Chen W. New RBF Collocation Schemes and Kernel RBFs with Applications. Lecture Notes in Computational Science and Engineering, vol. 26. Springer: Berlin, 2002; 75-86. Chen W. Symmetric boundary knot method. Engineering Analysis with Boundary Elements 2002; 26(6):489-494. Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn), vol. 3. Butterworth-Heinemann: London, 2000. Sadat H, Couturier S. Performance, accuracy of a meshless method for laminar natural convection. Numerical Heat Transfer, Part B 2000; 37:455-467. Atluri SN, Tulong Z. New concepts in meshless method. International Journal for Numerical Methods in Engineering 2000; 47:537-556. Yagawa G, Shirazaki M. Parallel computing for incompressible flow using a nodal-based method. Computational Mechanics 1999; 23:209-217. Chen W. Meshfree boundary particle method applied to Helmholtz problems. Engineering Analysis with Boundary Elements 2002; 26(7):577-581. Cheng M, Liu GR. A novel finite point method for flow simulation. International Journal for Numerical Methods in Fluids 2002; 39:1161-1178. Chorin AJ. Numerical solution of Navier-Stokes equations. Mathematics of Computation 1968; 22:745-762. Kawahara M, Ohmiya K. Finite element analysis of density flow using the velocity correction method. International Journal for Numerical Methods in Fluids 1985; 5:981-993. Shamekhi A, Nai MH. Buckling analysis of circular FGM plate having variable thickness under uniform compression by mesh free method. International Journal of Computational Methods 2005; 2(3):327-340. Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158. Armaly BF, Durst F, Pereira JCF, Schonung B. Experimental and theoretical investigation of backward facing step flow. Journal of Fluid Mechanics 1983; 127:473-496. Currie IG. Fundamental Mechanics of Fluids (2nd edn). McGraw-Hill: New York, 1974. Kim DW, Kim YS. Point collocation methods using the fast moving least square reproducing kernel approximation. International Journal for Numerical Methods in Engineering 2003; 56(10):1445-1464. Liu WK, Jun S, Zhang Y. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106. Gingold RA, Monaghan JJ. Smooth particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 1977; 81:375-389. Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48(3):387-411. Chen W, Tanaka M. A meshless, exponential convergence, integration-free, and boundary-only RBF technique. Computers and Mathematics with Applications 2002; 43:379-391. Comini G, Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer, Part A 1972; 5:463-478. Liu GR. Mesh Free Methods (1st edn). CRS Press LLC: Boca Raton, FL, 2002. 2002; 39 1989; 1 2000; 47 1985; 5 2000; 3 1997; 24 1999; 23 2003; 58 1974 2002 1972; 5 1992; 10 1992; 34 1968; 22 1977; 82 1977; 81 2003; 56 1995; 20 1983; 127 2002; 26 1982; 48 2000; 37 2002; 43 1981; 37 2005; 2 e_1_2_1_22_2 e_1_2_1_23_2 e_1_2_1_20_2 e_1_2_1_21_2 e_1_2_1_26_2 e_1_2_1_27_2 Currie IG (e_1_2_1_32_2) 1974 e_1_2_1_24_2 e_1_2_1_25_2 Zienkiewicz OC (e_1_2_1_28_2) 1989 e_1_2_1_29_2 e_1_2_1_6_2 e_1_2_1_30_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_3_2 e_1_2_1_12_2 e_1_2_1_10_2 e_1_2_1_31_2 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_17_2 e_1_2_1_9_2 e_1_2_1_18_2 |
| References_xml | – reference: Sadat H, Couturier S. Performance, accuracy of a meshless method for laminar natural convection. Numerical Heat Transfer, Part B 2000; 37:455-467. – reference: Ghia U, Ghia KN, Shin CT. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics 1982; 48(3):387-411. – reference: Lucy L. A numerical approach to testing the fission hypotheses. Astronomical Journal 1977; 82:1013-1024. – reference: Atluri SN, Tulong Z. New concepts in meshless method. International Journal for Numerical Methods in Engineering 2000; 47:537-556. – reference: Zienkiewicz OC, Taylor RL. The Finite Element Method (4th edn), vol. 1. McGraw-Hill: New York, 1989. – reference: Currie IG. Fundamental Mechanics of Fluids (2nd edn). McGraw-Hill: New York, 1974. – reference: Chen W. Symmetric boundary knot method. Engineering Analysis with Boundary Elements 2002; 26(6):489-494. – reference: Armaly BF, Durst F, Pereira JCF, Schonung B. Experimental and theoretical investigation of backward facing step flow. Journal of Fluid Mechanics 1983; 127:473-496. – reference: Liu WK, Jun S, Sihling DT, Chen YJ, Hao W. Multiresolution reproducing kernel particle method for computational fluid dynamics. International Journal for Numerical Methods in Fluids 1997; 24(12):1391-1415. – reference: Kim DW, Kim YS. Point collocation methods using the fast moving least square reproducing kernel approximation. International Journal for Numerical Methods in Engineering 2003; 56(10):1445-1464. – reference: Chorin AJ. Numerical solution of Navier-Stokes equations. Mathematics of Computation 1968; 22:745-762. – reference: Liu GR. Mesh Free Methods (1st edn). CRS Press LLC: Boca Raton, FL, 2002. – reference: Zienkiewicz OC, Taylor RL. The Finite Element Method (5th edn), vol. 3. Butterworth-Heinemann: London, 2000. – reference: Cheng M, Liu GR. A novel finite point method for flow simulation. International Journal for Numerical Methods in Fluids 2002; 39:1161-1178. – reference: Chen W, Tanaka M. A meshless, exponential convergence, integration-free, and boundary-only RBF technique. Computers and Mathematics with Applications 2002; 43:379-391. – reference: Comini G, Del Guidice S. Finite element solution of incompressible Navier-Stokes equations. Numerical Heat Transfer, Part A 1972; 5:463-478. – reference: Ramaswamy B, Jue TC, Akin JE. Semi-implicit and explicit finite element schemes for coupled fluid thermal problems. International Journal for Numerical Methods in Engineering 1992; 34:675-696. – reference: Yagawa G, Shirazaki M. Parallel computing for incompressible flow using a nodal-based method. Computational Mechanics 1999; 23:209-217. – reference: Zienkiewicz OC, Codina R. A general algorithm for compressible and incompressible flow. Part I. The split characteristic based scheme. International Journal for Numerical Methods in Fluids 1995; 20:869-885. – reference: Shamekhi A, Nai MH. Buckling analysis of circular FGM plate having variable thickness under uniform compression by mesh free method. International Journal of Computational Methods 2005; 2(3):327-340. – reference: Kawahara M, Ohmiya K. Finite element analysis of density flow using the velocity correction method. International Journal for Numerical Methods in Fluids 1985; 5:981-993. – reference: Lancaster P, Salkauskas K. Surfaces generated by moving least squares methods. Mathematics of Computation 1981; 37:141-158. – reference: Chen W. New RBF Collocation Schemes and Kernel RBFs with Applications. Lecture Notes in Computational Science and Engineering, vol. 26. Springer: Berlin, 2002; 75-86. – reference: Gingold RA, Monaghan JJ. Smooth particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 1977; 81:375-389. – reference: Tsukanov I, Shapiro V, Zhang S. A meshfree method for incompressible fluid dynamics problems. International Journal for Numerical Methods in Engineering 2003; 58:127-158. – reference: Chen W. Meshfree boundary particle method applied to Helmholtz problems. Engineering Analysis with Boundary Elements 2002; 26(7):577-581. – reference: Liu WK, Jun S, Zhang Y. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids 1995; 20:1081-1106. – reference: Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 1992; 10:307-318. – volume: 26 start-page: 489 issue: 6 year: 2002 end-page: 494 article-title: Symmetric boundary knot method publication-title: Engineering Analysis with Boundary Elements – volume: 5 start-page: 981 year: 1985 end-page: 993 article-title: Finite element analysis of density flow using the velocity correction method publication-title: International Journal for Numerical Methods in Fluids – volume: 20 start-page: 869 year: 1995 end-page: 885 article-title: A general algorithm for compressible and incompressible flow. Part I. The split characteristic based scheme publication-title: International Journal for Numerical Methods in Fluids – volume: 3 year: 2000 – volume: 23 start-page: 209 year: 1999 end-page: 217 article-title: Parallel computing for incompressible flow using a nodal‐based method publication-title: Computational Mechanics – volume: 2 start-page: 327 issue: 3 year: 2005 end-page: 340 article-title: Buckling analysis of circular FGM plate having variable thickness under uniform compression by mesh free method publication-title: International Journal of Computational Methods – start-page: 703 end-page: 708 – volume: 1 year: 1989 – volume: 34 start-page: 675 year: 1992 end-page: 696 article-title: Semi‐implicit and explicit finite element schemes for coupled fluid thermal problems publication-title: International Journal for Numerical Methods in Engineering – start-page: 75 year: 2002 end-page: 86 – volume: 48 start-page: 387 issue: 3 year: 1982 end-page: 411 article-title: High‐Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method publication-title: Journal of Computational Physics – volume: 22 start-page: 745 year: 1968 end-page: 762 article-title: Numerical solution of Navier–Stokes equations publication-title: Mathematics of Computation – volume: 26 start-page: 577 issue: 7 year: 2002 end-page: 581 article-title: Meshfree boundary particle method applied to Helmholtz problems publication-title: Engineering Analysis with Boundary Elements – volume: 81 start-page: 375 year: 1977 end-page: 389 article-title: Smooth particle hydrodynamics: theory and application to non‐spherical stars publication-title: Monthly Notices of the Royal Astronomical Society – volume: 37 start-page: 455 year: 2000 end-page: 467 article-title: Performance, accuracy of a meshless method for laminar natural convection publication-title: Numerical Heat Transfer, Part B – volume: 43 start-page: 379 year: 2002 end-page: 391 article-title: A meshless, exponential convergence, integration‐free, and boundary‐only RBF technique publication-title: Computers and Mathematics with Applications – start-page: 1009 end-page: 1014 – volume: 82 start-page: 1013 year: 1977 end-page: 1024 article-title: A numerical approach to testing the fission hypotheses publication-title: Astronomical Journal – volume: 58 start-page: 127 year: 2003 end-page: 158 article-title: A meshfree method for incompressible fluid dynamics problems publication-title: International Journal for Numerical Methods in Engineering – volume: 127 start-page: 473 year: 1983 end-page: 496 article-title: Experimental and theoretical investigation of backward facing step flow publication-title: Journal of Fluid Mechanics – volume: 37 start-page: 141 year: 1981 end-page: 158 article-title: Surfaces generated by moving least squares methods publication-title: Mathematics of Computation – year: 2002 – volume: 5 start-page: 463 year: 1972 end-page: 478 article-title: Finite element solution of 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| Snippet | This study presents characteristic‐based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was... This study presents characteristic-based split (CBS) algorithm in the meshfree context. This algorithm is the extension of general CBS method which was... |
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| SubjectTerms | characteristic-based split algorithm Computational methods in fluid dynamics Exact sciences and technology finite element method Fluid dynamics fluid flow Fundamental areas of phenomenology (including applications) meshfree method Physics |
| Title | On the use of characteristic-based split meshfree method for solving flow problems |
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