A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows (Advances in Applied Mathematics and Mechanics, 2023)
A computational code is developed for the numerical solution of one-dimensional transient gas-liquid flows using drift-flux models, in isothermal and alsowith phase change situations. For these two-phase models, classical upwind schemessuch as Roe- and Godunov-type schemes are generally difficult to derive and expensive to use, since there are no treatable analytic expressions for the Jacobian matrix,eigenvalues and eigenvectors of the system of equations. On the other hand, the high-order compact finite difference scheme becomes an attractive alternative on these occasions, as it does not make use of any wave propagation information from the systemof equations. The present paper extends the localized artificial diffusivity method forhigh-order compact finite difference schemes to solve two-phase flows with discontinuities. The numerical method has simple formulation, straightforward implementation, low computational cost and, most importantly, high-accuracy. The numerical methodology proposed is validated by solving several numerical examples givenin the literature. The simulations are sixth-order accurate and it is shown that theproposed numerical method provides accurate approximations of shock waves andcontact discontinuities. This is an essential property for simulations of realistic masstransport problems relevant to operations in the petroleum industry.