Characteristic-based split (CBS) algorithm finite element modelling for shallow waters in the Venice lagoon
In this paper, the characteristic‐based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations are the well‐known vertically integrated shallow‐water equations expressed in terms of total water depth and horizontal velocities. The appr...
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| Published in | International journal for numerical methods in engineering Vol. 66; no. 10; pp. 1641 - 1657 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
04.06.2006
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0029-5981 1097-0207 |
| DOI | 10.1002/nme.1690 |
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| Abstract | In this paper, the characteristic‐based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations are the well‐known vertically integrated shallow‐water equations expressed in terms of total water depth and horizontal velocities. The approximation of any additional scalar variables, such as temperature, concentration or pollutant dispersion from the appropriate advection–diffusion governing equations is also outlined. Numerical results illustrate the performance of the proposed algorithm on both advection–diffusion and shallow‐water problems. Copyright © 2006 John Wiley & Sons, Ltd. |
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| AbstractList | In this paper, the characteristic‐based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations are the well‐known vertically integrated shallow‐water equations expressed in terms of total water depth and horizontal velocities. The approximation of any additional scalar variables, such as temperature, concentration or pollutant dispersion from the appropriate advection–diffusion governing equations is also outlined. Numerical results illustrate the performance of the proposed algorithm on both advection–diffusion and shallow‐water problems. Copyright © 2006 John Wiley & Sons, Ltd. In this paper, the characteristic-based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations are the well-known vertically integrated shallow-water equations expressed in terms of total water depth and horizontal velocities. The approximation of any additional scalar variables, such as temperature, concentration or pollutant dispersion from the appropriate advection-diffusion governing equations is also outlined. Numerical results illustrate the performance of the proposed algorithm on both advection-diffusion and shallow- water problems. |
| Author | Venturin, M. Morandi-Cecchi, M. |
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| Cites_doi | 10.1142/9789812812957_0053 10.1002/fld.1650200812 10.1002/(SICI)1097-0363(199801)27:1/4<81::AID-FLD651>3.0.CO;2-O 10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P 10.1090/S0025-5718-1969-0242393-5 10.1002/nme.1620220305 10.1002/0470013826 10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7 10.1090/S0025-5718-1968-0242392-2 10.1002/fld.1650200823 10.1007/BF00247696 10.1016/S0045-7825(97)00138-2 |
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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. Stoker JJ. Water Waves. Interscience Publishers Inc. Interscience Publishers Inc.: New York, 1957. Colli P, Verdi C, Visintin A (eds). Free Boundary Problems: Theory and Applications. ISNM, vol. 147. Birkhäuser: Basel. Morandi-Cecchi M, Salasnich L. Shallow water theory and its application to the Venice lagoon. Computer Methods in Applied Mechanics and Engineering 1998; 151:63-74. Peraire J, Zienkiewicz OC, Morgan K. Shallow water problems: a general explicit formulation. International Journal for Numerical Methods in Engineering 1986; 22:547-574. Chorin AJ. On the convergence of discrete approximations to the Navier-Stokes equations. Mathematics of Computation 1969; 23(106):341-353. Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22(104):745-762. Morandi-Cecchi M, Pica A, Secco E. A projection methods for shallow water equations. International Journal for Numerical Methods in Fluids 1998; 27(25):81-95. Donea J, Huerta A. Finite Element Methods for Flow Problems. Wiley: Chichester, 2003. Zienkiewicz OC, Nithiarasu P, Codina R, Vazquez M, Ortiz P. The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems. International Journal for Numerical Methods in Fluids 1999; 31:359-392. Zienkiewicz OC, Ortiz P. A split-characteristic based finite element model for the shallow water equations. International Journal for Numerical Methods in Engineering 1995; 20:1061-1080. Zienkiewicz OC, Taylor RL. The Finite Element Method, vol. 3 (5th edn). Butterworth-Heinemann: London, 2000. Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. II. Archive for Rational Mechanics and Analysis 1969; 33:377-385. Lewis RW, Morgan K, Thomas HR, Seetharamu KN. The Finite Element Method in Heat Transfer Analysis. Wiley: Chichester, 1996. 1998; 27 1995; 20 2000; 3 1986; 22 1998 1969; 23 1969; 33 1996 1999; 31 2004 1993 2003 1998; 151 1968; 22 1957 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 D'Alpaos L (e_1_2_1_18_2) 1993 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_3_2 Lewis RW (e_1_2_1_17_2) 1996 Chorin AJ (e_1_2_1_10_2) 1969; 23 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 Colli P (e_1_2_1_14_2) Stoker JJ (e_1_2_1_12_2) 1957 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – reference: Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22(104):745-762. – reference: Stoker JJ. Water Waves. Interscience Publishers Inc. Interscience Publishers Inc.: New York, 1957. – reference: Zienkiewicz OC, Nithiarasu P, Codina R, Vazquez M, Ortiz P. The characteristic-based-split procedure: an efficient and accurate algorithm for fluid problems. International Journal for Numerical Methods in Fluids 1999; 31:359-392. – reference: Peraire J, Zienkiewicz OC, Morgan K. Shallow water problems: a general explicit formulation. International Journal for Numerical Methods in Engineering 1986; 22:547-574. – reference: Morandi-Cecchi M, Salasnich L. Shallow water theory and its application to the Venice lagoon. Computer Methods in Applied Mechanics and Engineering 1998; 151:63-74. – reference: Zienkiewicz OC, Taylor RL. The Finite Element Method, vol. 3 (5th edn). Butterworth-Heinemann: London, 2000. – reference: Donea J, Huerta A. Finite Element Methods for Flow Problems. Wiley: Chichester, 2003. – reference: Colli P, Verdi C, Visintin A (eds). Free Boundary Problems: Theory and Applications. ISNM, vol. 147. Birkhäuser: Basel. – reference: Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires. II. Archive for Rational Mechanics and Analysis 1969; 33:377-385. – reference: Zienkiewicz OC, Ortiz P. A split-characteristic based finite element model for the shallow water equations. International Journal for Numerical Methods in Engineering 1995; 20:1061-1080. – reference: Morandi-Cecchi M, Pica A, Secco E. A projection methods for shallow water equations. International Journal for Numerical Methods in Fluids 1998; 27(25):81-95. – 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: Chorin AJ. On the convergence of discrete approximations to the Navier-Stokes equations. Mathematics of Computation 1969; 23(106):341-353. – reference: Lewis RW, Morgan K, Thomas HR, Seetharamu KN. The Finite Element Method in Heat Transfer Analysis. Wiley: Chichester, 1996. – volume: 22 start-page: 745 issue: 104 year: 1968 end-page: 762 article-title: Numerical solution of the Navier–Stokes equations publication-title: Mathematics of Computation – volume: 33 start-page: 377 year: 1969 end-page: 385 article-title: Sur l'approximation de la solution des équations de Navier–Stokes par la méthode des pas fractionnaires. II publication-title: Archive for Rational Mechanics and Analysis – year: 1957 – volume: 31 start-page: 359 year: 1999 end-page: 392 article-title: The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems publication-title: International Journal for Numerical Methods in Fluids – volume: 151 start-page: 63 year: 1998 end-page: 74 article-title: Shallow water theory and its application to the Venice lagoon publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 23 start-page: 341 issue: 106 year: 1969 end-page: 353 article-title: On the convergence of discrete approximations to the Navier–Stokes equations publication-title: Mathematics of Computation – start-page: 917 year: 1993 end-page: 926 – volume: 20 start-page: 1061 year: 1995 end-page: 1080 article-title: A split‐characteristic based finite element model for the shallow water equations publication-title: International Journal for Numerical Methods in Engineering – volume: 3 year: 2000 – volume: 27 start-page: 81 issue: 25 year: 1998 end-page: 95 article-title: A projection methods for shallow water equations publication-title: International Journal for Numerical Methods in Fluids – year: 2004 – year: 2003 – year: 1996 – start-page: 972 year: 1998 end-page: 993 – 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: 22 start-page: 547 year: 1986 end-page: 574 article-title: Shallow water problems: a general explicit formulation publication-title: International Journal for Numerical Methods in Engineering – ident: e_1_2_1_4_2 doi: 10.1142/9789812812957_0053 – ident: e_1_2_1_6_2 doi: 10.1002/fld.1650200812 – ident: e_1_2_1_2_2 doi: 10.1002/(SICI)1097-0363(199801)27:1/4<81::AID-FLD651>3.0.CO;2-O – ident: e_1_2_1_8_2 doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P – volume: 23 start-page: 341 issue: 106 year: 1969 ident: e_1_2_1_10_2 article-title: On the convergence of discrete approximations to the Navier–Stokes equations publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1969-0242393-5 – ident: e_1_2_1_13_2 doi: 10.1002/nme.1620220305 – ident: e_1_2_1_16_2 doi: 10.1002/0470013826 – ident: e_1_2_1_7_2 doi: 10.1002/(SICI)1097-0363(19990915)31:1<359::AID-FLD984>3.0.CO;2-7 – ident: e_1_2_1_9_2 doi: 10.1090/S0025-5718-1968-0242392-2 – volume-title: Water Waves year: 1957 ident: e_1_2_1_12_2 – volume-title: The Finite Element Method in Heat Transfer Analysis year: 1996 ident: e_1_2_1_17_2 – ident: e_1_2_1_19_2 – volume-title: Free Boundary Problems: Theory and Applications ident: e_1_2_1_14_2 – ident: e_1_2_1_5_2 doi: 10.1002/fld.1650200823 – ident: e_1_2_1_15_2 – ident: e_1_2_1_11_2 doi: 10.1007/BF00247696 – ident: e_1_2_1_3_2 doi: 10.1016/S0045-7825(97)00138-2 – start-page: 917 volume-title: Finite Elements in Fluids year: 1993 ident: e_1_2_1_18_2 |
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| Snippet | In this paper, the characteristic‐based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations... In this paper, the characteristic-based split (CBS) algorithm is presented to solve water motion problem due to tides in the Venice lagoon. The basic equations... |
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| SubjectTerms | Algorithms Approximation CBS algorithm Dispersions finite element method fluid dynamics Lagoons Mathematical analysis Mathematical models Scalars shallow-water equations shallow-water problems Water depth |
| Title | Characteristic-based split (CBS) algorithm finite element modelling for shallow waters in the Venice lagoon |
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