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. Figure 4. Comparison of the numerical solution for the velocity with the reference presented in [17] for t = 0.8 s. (a) Upwind; (b) Lax Wendroff + van Leer limiter.

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Este trabalho não poderia ser terminado sem a ajuda de diversas pessoas às quais presto minha homenagem: Aos meus pais pelo apoio incondicional em todos os momentos da minha vida.Aos meus irmãos Luciano e Thiago.Ao meu orientador Luiz Fernando Milanez, pela confiança depositada em mim.