Well-Posedness for Two-Fluid Two-Phase Flow Equations

Abstract

This paper presents the contribution of the second-order spatial differential terms to the well-posedness of two-fluid model, assuming that one pressure is set for each cell in a one-dimensional two-phase flow system. According to the results of the numerical calculation by applying Hadamard condition, second-order spatial differential term makes the given equation system well-posed as the initial value problem in case the momentum equation is endowed with second-order spatial differential term.
Such a condition cannot be always applied to judge the well-posedness if the equation system is hyperbolic and coefficient matrix of the differential term with respect to time is singular, the determinant of the matrix is zero.
As described in this paper, with regard to a differential equation system whose differential terms, including second-order spatial differential terms, are converted into first or zero-order terms, it is necessary for the characteristic equation not to be eliminated zero-order term to evaluate the well-posedness by examining the bounded of real part of the characteristic root.