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Roe‐type Riemann solver for gas–liquid flows using drift‐flux model with an approximate form of the Jacobian matrix
Author(s) -
Silva Santim Christiano Garcia,
Rosa Eugênio Spanó
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4165
Subject(s) - riemann solver , roe solver , mathematics , jacobian matrix and determinant , solver , linearization , eigenvalues and eigenvectors , mathematical analysis , riemann hypothesis , riemann problem , finite volume method , physics , mathematical optimization , mechanics , nonlinear system , quantum mechanics
Summary This work presents an approximate Riemann solver to the transient isothermal drift ‐ flux model. The set of equations constitutes a non‐linear hyperbolic system of conservation laws in one space dimension. The elements of the Jacobian matrix A are expressed through exact analytical expressions. It is also proposed a simplified form of A considering the square of the gas to liquid sound velocity ratio much lower than one. This approximation aims to express the eigenvalues through simpler algebraic expressions. A numerical method based on the Gudunov's fluxes is proposed employing an upwind and a high order scheme. The Roe linearization is applied to the simplified form of A . The proposed solver is validated against three benchmark solutions and two experimental pipe flow data. Copyright © 2015 John Wiley & Sons, Ltd.