A fractional step method to compute a class of compressible gas–liquid flows

Abstract We present in this paper some algorithms dedicated to the computation of numerical approximations of a class of two-fluid two-phase flow models. Governing equations for the statistical void fraction, partial mass, momentum, energy are presented first, and meaningful closure laws are given. Then we may give the main properties of the class of two-fluid models. The whole algorithm that relies on the fractional step method and complies with the entropy inequality is presented afterwards. Emphasis is given on the computation of pressure–velocity–temperature relaxation source terms. Conditions pertaining to the existence and uniqueness of discrete solutions of the relaxation step are given. While focusing on some one-dimensional test cases, the true rates of convergence may be obtained within the evolution step and the relaxation step. Eventually, some two-dimensional numerical simulations of a heated wall are shown and are briefly discussed. Some advantages and weaknesses of algorithms are also discussed.

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