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Finite element methods for geothermal reservoir simulation
Author(s) -
Zyvoloski George
Publication year - 1983
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610070108
Subject(s) - finite element method , discretization , mathematics , mass matrix , matrix (chemical analysis) , solver , algebraic equation , newton's method , mixed finite element method , extended finite element method , geothermal gradient , multigrid method , mathematical optimization , computer science , partial differential equation , mathematical analysis , nonlinear system , geology , engineering , physics , structural engineering , materials science , quantum mechanics , neutrino , geophysics , nuclear physics , composite material
Two finite element algorithms suitable for long term simulation of geothermal reservoirs are presented. Both methods use a diagonal mass matrix and a Newton iteration scheme. The first scheme solves the 2 N unsymmetric algebraic equations resulting from the finite element discretization of the equations governing the flow of heat and mass in porous media by using a banded equation solver. The second method, suitable for problems in which the transmissibility terms are small compared to the accumulation terms, reduces the set of N equations for the Newton corrections to a symmetric system. Comparison with finite difference schemes indicates that the proposed algorithms are competitive with existing methods.

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