Applications of the modified Trefftz method to the simulation of sloshing behaviours

Engineering Analysis with Boundary Elements

Volumn 34, Issue 6, 2010, Pages 581-598

  Chen, Yung Wei ^a   Liu, Chein Shan ^a   Chang, Chun Ming ^a   Chang, Jiang Ren ^a  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

Laplace equation; Mixed boundary value problem; Modified Trefftz method; Sloshing

Indexed keywords

CHARACTERISTIC LENGTH; COEFFICIENT MATRIX; CONTROLLED VOLUME; FREE SURFACES; ILL POSED; MIXED BOUNDARY-VALUE PROBLEM; MODIFIED TREFFTZ METHOD; NON-LINEAR; NUMERICAL DISSIPATION; NUMERICAL EFFICIENCY; NUMERICAL INSTABILITY; NUMERICAL PROCEDURES; NUMERICAL RESULTS; SECOND ORDER DERIVATIVES; VELOCITY POTENTIALS; WEIGHTING FACTORS;

GLOBAL POSITIONING SYSTEM; INTEGRODIFFERENTIAL EQUATIONS; LAPLACE EQUATION; LAPLACE TRANSFORMS; NUMBER THEORY; NUMERICAL ANALYSIS; TWO DIMENSIONAL;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77949288688     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2010.01.003     Document Type: Article

References (27)

1. Abramson HN. The dynamic behaviour of liquids in moving containers. Report SP106 of NASA 1966.
2. Faltinsen O.M. A nonlinear theory of sloshing in rectangular tanks. J Ship Res 18 (1974) 224-241
3. Solaas F., and Faltinsen O.M. Combiner numerical solution for sloshing in two-dimensional tanks of general shape. J Ship Res 41 (1997) 118-129
4. Chen W., Haroun M., and Liu F. Large amplitude liquid sloshing in seismically excited tanks. Earthquake Eng Struct Dyn 25 (1996) 653-669
5. Chen B.F., and Chiang H.W. Complete two-dimensional analysis of sea-wave-induced fully nonlinear sloshing fluid in a rigid floating tank. Ocean Eng 27 (2000) 953-977
6. Ikegawa M. Finite element analysis of fluid motion in a container. In: Finite element methods in flow problems. Huntsville, Alabama: UAH Press;1974. p. 737-8.
7. Nakayam T., and Washizu K. Nonlinear analysis of liquid motion in a container subjected to a forced pitching oscillation. Int J Numer Method Eng 15 (1980) 1207-1220
8. Zhou H., Li J.F., and Wang T.S. Simulation of liquid sloshing in curved-wall containers with arbitrary Lagrangian-Eulerian method. Int J Numer Method Fluids 57 (2008) 437-452
9. Mitra S., Upadhyay P.P., and Sinhamahapatra K.P. Slosh dynamics of inviscid fluids in two-dimensional tanks of various geometry using finite element method. Int J Numer Method Fluids 56 (2008) 1625-1651
10. Faltinsen O.M. A numerical non-linear method of sloshing in tanks with two-dimensional flow. J Ship Res 22 (1978) 193-202
11. Nakayam T., and Washizu K. The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems. Int J Numer Method Eng 17 (1981) 631-646
12. Romero V.J., and Ingber M.S. A numerical model for 2-D Sloshing of pseudoviscous liquids in horizontally accelerated rectangular containers. Bound Elem XVII (1995) 567-583
13. Chen Y.H., Hwang W.S., and Ko C.H. Numerical simulation of the three-dimensional sloshing problem by boundary element method. J Chin Inst Eng 23 (2000) 321-330
14. Chen Y.H., Hwang W.S., and Ko C.H. Sloshing behaviors of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations. Earthquake Eng Struct Dyn 36 (2007) 1701-1717
15. Monaghan J.J. Simulating free surface flows with SPH. J Comput Phys 110 (1994) 399-406
16. Ma Q.W. Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems. J Comput Phys 205 (2005) 611-625
17. Ali A., Mohammad N., and Hooman A. A meshless local Petrov-Galerkin method for fluid dynamics and heat transfer applications. J Fluids Eng 127 (2005) 647-655
18. Vaughan G.L., Healy T.R., Bryan K.R., Sneyd A.D., and Gorman R.M. Completeness, Conservation and Error in SPH for fluids. Int J Numer Method Fluids 56 (2008) 37-62
19. Jan A.K., and Magdalena M. The application of the method of fundamental solutions to a simulation of the two-dimensional sloshing phenomenon. J Mech Mater Struct 3 6 (2008) 1087-1095
20. Trefftz E. Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings of the second international congress on Applied Mechanics, Zurich, 1926. p. 131-7.
21. Herrera I., Theory of connectivity: a systematic formulation of boundary element methods, In: Brebbia CA, editor. New developments in boundary element methods (Proceedings of the second international seminar on recent advances in BEM, Southampton, England, 1980). Plymouth: Pentech Press; 1980. p. 45-58
22. Kita E., Katsuragawa J., and Kamiya N. Application of Trefftz-type boundary element method to simulation of two-dimensional sloshing phenomenon. Eng Anal Bound Elem 28 (2004) 677-683
23. Liu C.S. A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length. Comp Model Eng Sci 21 (2007) 53-65
24. Liu C.S. Cone of non-linear dynamical system and group preserving schemes. Int J Non-Linear Mech 36 (2001) 1047-1068
25. Liu C.S. A highly accurate MCTM for inverse Cauchy problems of Laplace equation in arbitrary plane domains. Comp Model Eng Sci 35 (2008) 91-111
26. Wasizu K., Nakayama T., Ikegawa M., Tanaka Y., and Adachi T. Some finite element for techniques analysis of nonlinear sloshing problem (1984), Wiley, New York p. 357-376; (chapter 5)
27. Chen B.F., and Chiang H.W. Complete 2D and fully nonlinear analysis of ideal fluid in tanks. J Eng Mech 125 (1999) 70-78