Finite element methods for an acoustic well‐logging problem associated with a porous medium saturated by a two‐phase immiscible fluid | Zendy

Sheen Dongwoo | Zendy

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Finite element methods for an acoustic well‐logging problem associated with a porous medium saturated by a two‐phase immiscible fluid

Author(s) -

Sheen Dongwoo

Publication year - 1993

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.1690090205

Subject(s) - inviscid flow , compressibility , uniqueness , boundary value problem , porous medium , finite element method , convergence (economics) , mathematics , domain (mathematical analysis) , mechanics , boundary (topology) , mathematical analysis , porosity , stability (learning theory) , phase (matter) , geology , physics , thermodynamics , geotechnical engineering , computer science , quantum mechanics , machine learning , economic growth , economics

A mathematical model is presented concerning wave propagation in a domain that arises in geophysical well‐logging problems. The domain consists of a borehole Ω f surrounded by a porous medium Ω p . Ω f is filled with a compressible inviscid fluid, and Ω p is saturated by a two‐phase immiscible fluid. Absorbing boundary conditions for artificial boundaries and boundary conditions on the interface between Ω f and Ω p are used. The existence and uniqueness theorems are stated for the resulting initial‐boundary value problem. Stability and convergence estimates for a finite element method are also studied. © 1993 John Wiley & Sons, Inc.

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