Scientific Computing and Numerics (SCAN) Seminar
When simulating interfacial two-phase flows, e.g., gas-liquid flows, the temporal evolution of the interface between the two immiscible phases requires dedicated numerical schemes, designed to retain a sharp and conservative representation of the phases’ indicator function. Currently, the state-of-the-art numerical methods rely on piecewise-linear approximations of the interface for reconstructing the fluxes of the indicator function. As a result, the accuracy of the discrete indicator function (i.e., of the phase volume-fractions) is limited to second-order at best, while that of the interface curvature is limited to zeroth-order. In this talk, we extend this traditional approach by considering piecewise-parabolic interface approximations instead of piecewise-linear ones. To that end, we derive closed-form expressions for the first moments of any arbitrary polyhedron clipped by a paraboloid. This enables the formulation of the parabolic interface reconstruction problem as a minimization of moment errors, as well as the efficient and conservative transport of the phases’ indicator function using a semi-Lagrangian advection scheme. We study the convergence of our new framework and provide examples of its application to two-phase flows that are driven by surface-tension.