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42              3  Algorithm for Simulating Coupled Problems in Hydrothermal Systems

            Within the first sub-problem itself, the pore-fluid flow is coupled with the thermal
            flow and reactive flow through the medium temperature, aqueous chemical species
            concentrations and pore-fluid velocity components, u and v. However, within the
            second sub-problem itself, the medium deformation (displacement) is coupled with
            the medium temperature, pore-fluid pressure and permeability through the volumet-
            ric strain, ε v , and the medium porosity, φ.
              With regard to the general solution method used in this study, FIDAP (Fluid
            Dynamics International 1997), which is one of the most powerful finite element
            codes currently available for dealing with a very wide range of practical prob-
            lems in fluid dynamics, is used to solve the first sub-problem, while FLAC (Itasca
            Consulting Group 1995), which is a very useful finite difference code for dealing
            with material deformation problems in the fields of both geotechnical engineering
            and geoscience, is used to solve the second sub-problem. A general interface pro-
            gram is developed to translate and transfer data between FIDAP and FLAC. To
            obtain non-trivial (convective) solutions for the pore-fluid flow under supercritical
            Rayleigh number conditions, the progressive asymptotic approach procedure dis-
            cussed in Chap. 2 (Zhao et al. 1997a) is also employed in the computation.



            3.2 Mathematical Formulation of the Consistent Point-Searching
                Interpolation Algorithm in Unstructured Meshes

            The motivation of developing a consistent point-searching interpolation algorithm
            is described as follows. For two totally different meshes, namely mesh 1 (mesh in
            FIDAP) and mesh 2 (mesh in FLAC) shown in Fig. 3.1, finite element solutions
            to the temperature and pressure due to hydrothermal effects are available (from
            FIDAP) at the nodal points of mesh 1 but not known at those of mesh 2. This


























            Fig. 3.1 Two totally different meshes used in FIDAP and FLAC
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