Multiquadric method for the numerical solution of a biphasic mixture model
A computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model. The model includes a set of constitutive equations for the fluid flows through the solid phase; a set of momentum equations for stress-strain equilibrium and a continuity equation for the...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 88; H. 2; S. 153 - 175 |
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| Sprache: | Englisch |
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1997
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | A computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model. The model includes a set of constitutive equations for the fluid flows through the solid phase; a set of momentum equations for stress-strain equilibrium and a continuity equation for the solid phase and the fluid phase. The numerical method does not require the generation of mesh as in the finite element method and hence gives high flexibility in applying the method to irregular geometry. Numerical examples are made to compute the solution of the confined compression problem which approximates the nonlinear response of soft hydrated tissues under external loading. The numerical results are compared with Spilker's penalty finite element method. |
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| AbstractList | A computational algorithm based on the multiquadric method has been devised to solve the biphasic mixture model. The model includes a set of constitutive equations for the fluid flows through the solid phase; a set of momentum equations for stress-strain equilibrium and a continuity equation for the solid phase and the fluid phase. The numerical method does not require the generation of mesh as in the finite element method and hence gives high flexibility in applying the method to irregular geometry. Numerical examples are made to compute the solution of the confined compression problem which approximates the nonlinear response of soft hydrated tissues under external loading. The numerical results are compared with Spilker's penalty finite element method. |
| Author | Xue, W.M. Zhu, Y.M. Hon, Y.C. Lu, M.W. |
| Author_xml | – sequence: 1 givenname: Y.C. surname: Hon fullname: Hon, Y.C. organization: Department of Mathematics City University of Hong Kong Hong Kong – sequence: 2 givenname: M.W. surname: Lu fullname: Lu, M.W. organization: Department of Engineering Mechanics Tsinghua University People's Republic of China – sequence: 3 givenname: W.M. surname: Xue fullname: Xue, W.M. – sequence: 4 givenname: Y.M. surname: Zhu fullname: Zhu, Y.M. |
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| Cites_doi | 10.1016/0021-9290(84)90031-9 10.1016/0898-1221(90)90271-K 10.1115/1.2895793 10.1002/nme.1620320704 10.1029/JB076i008p01905 10.1115/1.3554924 10.1016/0096-3003(94)90099-X 10.1016/0898-1221(92)90175-H 10.1115/1.3138565 10.1137/0722040 10.1016/0021-9290(76)90071-3 10.1243/PIME_PROC_1991_205_286_02 10.1007/BF02547926 10.1016/0021-9290(87)90147-3 10.1016/0045-7949(90)90067-C |
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| Keywords | Constitutive equation Finite element method Biphasic system Grid pattern Continuity equation Numerical solution Mixture theory Numerical method Nonlinear problems Algorithm Equilibrium equation Partial differential equation |
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| References | Tarwater (BIB17) Sept. 1985 Simon, Wu, Carlton, Evans, Kazarian (BIB5) 1985; 107 Hardy (BIB13) 1971; 176 Suh, Spilker, Holmes (BIB2) 1991; 32 Franke (BIB14) 1982; 38 Mow (BIB4) 1969; 91 Kenyon (BIB8) 1979; 41 Hon, Huang, Lu, Mak, Xue (BIB12) 1996; 4 Wayne, Woo, Kwan (BIB11) 1992; 205 Kansa (BIB15) 1990; 19 Mak, Huang, Wang (BIB10) 1994; 116 Golberg, Chen (BIB19) 1994; 60 Torzilli, Mow (BIB3) 1976; 9 Oomens, VanCampen, Grootenboer (BIB9) 1982; 20 Madych (BIB18) 1992; 24 Cheng (BIB21) 1987 Salzetein, Pollack, Mak, Petron, Brankov (BIB6) 1987; 20 Bogomonly (BIB20) 1985; 22 Taber, Yang, Keller, Clark (BIB7) 1992 Mow, Holmes, Lai (BIB16) 1984; 17 Spilker, Suh (BIB1) 1990; 35 Kansa (10.1016/S0096-3003(96)00309-8_BIB15) 1990; 19 Salzetein (10.1016/S0096-3003(96)00309-8_BIB6) 1987; 20 Tarwater (10.1016/S0096-3003(96)00309-8_BIB17) 1985 Bogomonly (10.1016/S0096-3003(96)00309-8_BIB20) 1985; 22 Kenyon (10.1016/S0096-3003(96)00309-8_BIB8) 1979; 41 Suh (10.1016/S0096-3003(96)00309-8_BIB2) 1991; 32 Oomens (10.1016/S0096-3003(96)00309-8_BIB9) 1982; 20 Mak (10.1016/S0096-3003(96)00309-8_BIB10) 1994; 116 Hon (10.1016/S0096-3003(96)00309-8_BIB12) 1996; 4 Mow (10.1016/S0096-3003(96)00309-8_BIB4) 1969; 91 Torzilli (10.1016/S0096-3003(96)00309-8_BIB3) 1976; 9 Simon (10.1016/S0096-3003(96)00309-8_BIB5) 1985; 107 Wayne (10.1016/S0096-3003(96)00309-8_BIB11) 1992; 205 Golberg (10.1016/S0096-3003(96)00309-8_BIB19) 1994; 60 Mow (10.1016/S0096-3003(96)00309-8_BIB16) 1984; 17 Hardy (10.1016/S0096-3003(96)00309-8_BIB13) 1971; 176 Franke (10.1016/S0096-3003(96)00309-8_BIB14) 1982; 38 Taber (10.1016/S0096-3003(96)00309-8_BIB7) 1992 Madych (10.1016/S0096-3003(96)00309-8_BIB18) 1992; 24 Cheng (10.1016/S0096-3003(96)00309-8_BIB21) 1987 Spilker (10.1016/S0096-3003(96)00309-8_BIB1) 1990; 35 |
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| SubjectTerms | Algorithms for functional approximation Exact sciences and technology Mathematical methods in physics Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation and analysis Numerical differentiation and integration Partial differential equations, boundary value problems Physics Sciences and techniques of general use |
| Title | Multiquadric method for the numerical solution of a biphasic mixture model |
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