Conservative semi-Lagrangian CIP technique for the shallow water equations

Computational Mechanics

Volumn 46, Issue 1, 2010, Pages 125-134

  Yabe, Takashi ^a   Ogata, Youichi ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

CIP method; Conservation; Method of characteristics; Semi Lagrangian; Shallow water equations

Indexed keywords

CONSERVATION; INTERPOLATION; LAGRANGE MULTIPLIERS; NUMERICAL METHODS;

CIP METHODS; CONSERVATION PROPERTIES; CONSTRAINED INTERPOLATION PROFILES; METHOD OF CHARACTERISTICS; ORDERS OF MAGNITUDE; SEMI-LAGRANGIAN; SHALLOW WATER EQUATIONS; SPLITTING TECHNIQUES;

EQUATIONS OF MOTION;

EID: 77951769332     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-009-0438-8     Document Type: Article

References (29)

1. A Arakawa VR Lamb 1981 A potential enstrophy and energy conserving scheme for the shallow water equations Mon Weather Rev 109 18 36 10.1175/1520- 0493(1981)109<0018:APEAEC>2.0.CO;2
2. K Kashiyama H Ito M Behr TE Tezduyar 1995 Three-step explicit finite element computation of shallow water flows on a massively parallel computer Int J Numer Meth Fluids 21 885 900 0861.76044 10.1002/fld.1650211009
3. K Kashiyama K Saitoh M Behr TE Tezduyar 1997 Parallel finite element methods for large-scale computation of storm surges and tidal flows Int J Numer Meth Fluids 24 1371 1389 0881.76052 10.1002/(SICI)1097-0363(199706)24: 12<1371::AID-FLD565>3.0.CO;2-7 (Pubitemid 27420085)
4. K Kashiyama Y Ohba T Takagi M Behr TE Tezduyar 1999 Parallel finite element method utilizing the mode splitting and sigma coordinate for shallow water flows Comput Mech 23 144 150 0949.76050 10.1007/s004660050394
5. TE Tezduyar 2001 Finite element methods for flow problems with moving boundaries and interfaces Arc Comput Methods Eng 8 83 130 1039.76037 10.1007/BF02897870 (Pubitemid 33303391)
6. PH Lauritzen E Kaas B Machenhauer 2006 A mass-conservative semi-implicit semi-Lagrangian limited-area shallow-water model on the sphere Mon Weather Rev 134 1205 1221 10.1175/MWR3115.1
7. A Staniforth J Côté 1991 Semi-Lagrangian integration schemes for atmospheric models-a review Mon Weather Rev 119 2206 2223 10.1175/1520-0493(1991)119<2206:SLISFA>2.0.CO;2
8. G Erbes 1993 A semi-Lagrangian method of characteristics for the shallow-water equations Mon Weather Rev 121 3443 3452 10.1175/1520-0493(1993) 121<3443:ASLMOC>2.0.CO;2
9. T Yabe T Aoki 1991 A universal solver for hyperbolic equations by cubic-polynomial interpolation. I. One-dimensional solver Comput Phys Commun 66 219 232 0991.65521 10.1016/0010-4655(91)90071-R 1125404 (Pubitemid 21710715)
10. T Yabe T Ishikawa PY Wang 1991 A universal solver for hyperbolic equations by cubic-polynomial interpolation. II. Two- and three-dimensional solver Comput Phys Commun 66 233 242 0991.65522 10.1016/0010-4655(91)90072-S 1125405 (Pubitemid 21710714)
11. Y Ogata T Yabe 2004 Multi-dimensional semi-Lagarangian characteristic approach to the shallow water equations by the CIP method Int J Comput Eng Sci 5 3 699 730 10.1142/S1465876304002642 (Pubitemid 40683645)
12. BP Leonard AP Lock MK Macvean 1996 Conservative explicit unstricted-time-step multidimensional constancy-preserving advection schemes Mon Weather Rev 124 2588 2606 10.1175/1520-0493(1996)124<2588:CEUTSM>2.0.CO;2
13. T Yabe F Xiao T Utsumi 2001 Constrained interpolation profile method for multiphase analysis J Comput Phys 169 556 593 1047.76104 10.1006/jcph.2000.6625 1836525 (Pubitemid 33665459)
14. T Yabe R Tanaka T Nakamura F Xiao 2001 An exactly conservative semi-Lagrangian scheme (CIP-CSL) in one dimension Mon Weather Rev 129 332 344 10.1175/1520-0493(2001)129<0332:AECSLS>2.0.CO;2 (Pubitemid 32546160)
15. R Tanaka T Nakamura T Yabe 2000 Constructing exactly conservative scheme in non-conservative form Comput Phys Commun 126 232 243 0959.65097 10.1016/S0010-4655(99)00473-7 1763694
16. T Nakamura R Tanaka T Yabe 2001 Multi-dimensional conservative scheme in non-conservative form CFD J 9 437 453
17. T Nakamura R Tanaka T Yabe K Takizawa 2001 Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique J Comput Phys 174 171 207 0995.65094 10.1006/jcph.2001.6888 1869674
18. K Toda Y Ogata T Yabe 2009 Multi-dimensional conservative semi-Lagrangian method of characteristics CIP for the shallow water equations J Comput Phys 228 4917 4944 1166.76045 10.1016/j.jcp.2009.04.003 2533163
19. Stoker J (1957) Water waves: the mathematical theory with applications. Interscience, New York
20. T Utsumi T Kunugi T Aoki 1997 Stability and accuracy of the cubic interpolated propagation scheme Comput Phys Commun 101 9 20 10.1016/S0010- 4655(96)00153-1 (Pubitemid 127428629)
21. H Takewaki T Yabe 1987 Cubic-interpolated pseudo particle (CIP) method : application to nonlinear or multi-dimensional problems J Comput Phys 70 355 372 0624.65079 10.1016/0021-9991(87)90187-2
22. Toro EF (1997) Riemann solvers and numerical methods for fluid dynamics. Springer, Berlin
23. DG Dritschel LM Polvani AR Mohebalhojeh 1999 The contour-advective semi-Lagrangian algorithm for the shallow water equations Mon Weather Rev 127 1551 1565 10.1175/1520-0493(1999)127<1551:TCASLA>2.0.CO;2 (Pubitemid 129656438)
24. R Sadourny 1972 Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids Mon Weather Rev 100 136 144 10.1175/1520-0493(1972)100<0136:CFAOTP>2.3.CO;2
25. C Chen F Xiao 2008 Shallow water model on cubed-sphere by multi-moment finite volume method J Comput Phys 227 5019 5044 05276060 10.1016/j.jcp.2008.01. 033 2414846
26. T Yabe H Mizoe K Takizawa H Moriki H-N Im Y Ogata 2004 Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme J Comput Phys 194 57 77 1049.76051 10.1016/j.jcp.2003.08.019 (Pubitemid 38184231)
27. K Takizawa T Yabe Y Tsugawa TE Tezduyar H Mizoe 2007 Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless soroban grids Comput Mech 40 167 183 1177.76300 10.1007/s00466-006-0093-2 (Pubitemid 46723553)
28. T Yabe K Takizawa TE Tezduyar H-N Im 2007 Computation of fluid-solid and fluid-fluid interfaces with the CIP method based on adaptive soroban grids-an overview Int J Numer Meth Fluids 54 841 853 05169596 10.1002/fld.1473 2333012 (Pubitemid 47009682)
29. K Takizawa K Tanizawa T Yabe TE Tezduyar 2007 Ship hydrodynamics computations with the CIP method based on adaptive soroban grids Int J Numer Meth Fluids 54 1011 1019 05169603 10.1002/fld.1466 (Pubitemid 47009689)