This paper is concerned with numerical solutions of the two-fluid models of two-phase flow. The two-fluid modeling approach is based on the effective-field description of inter-penetrating continua and uses constitutive laws to account for the inter-field interactions. The effective-field balance equations are derived by a homogenization procedure and known to be non-hyperbolic. Despite their importance and widespread application, predictions by such models have been hampered by numerical pitfalls manifested in the formidable challenge to obtain convergent numerical solutions under computational grid refinement. At the root of the problem is the absence of hyperbolicity in the field equations and the resulting ill-posedness. The aim of the present work is to develop a high-order-accurate numerical scheme that is not subject to such limitations. The main idea is to separate conservative and non-conservative parts, by implementing the latter as part of the source term. The conservative part, being effectively hyperbolic, is treated by a characteristics-based method. The scheme performance is examined on a compressible-incompressible two-fluid model. Convergence of numerical solutions to the analytical one is demonstrated on a benchmark (water faucet) problem.

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