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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Bibliographic Details
Published in:Applied mathematics and computation Vol. 88; no. 2; pp. 153 - 175
Main Authors: Hon, Y.C., Lu, M.W., Xue, W.M., Zhu, Y.M.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 1997
Elsevier
Subjects:
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
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
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(96)00309-8