A spectrally refined interface approach for simulating multiphase flows

This paper presents a novel approach to phase-interface transport based on pseudo-spectral sub-grid refinement of a level set function. In each flow solver grid cell, a set of quadrature points is introduced on which the value of the level set function is known. This methodology allows to define a polynomial reconstruction of the level set function in each cell. The transport is performed using a semi-Lagrangian technique, removing all constraints on the time step size. Such an approach provides sub-cell resolution of the phase-interface and leads to excellent accuracy in the transport, while a reasonable cost is obtained by pre-computing some of the metrics associated with the polynomials. To couple this approach with a flow solver, an converging curvature computation is introduced. First, a second order explicit distance to the sub-grid interface is reconstructed on the flow solver mesh. Then, a least squares approach is employed to extract the curvature from this distance function. This technique is found to combine the high accuracy and good conservation found in the particle level set method with the converging curvature usually obtained with classical high order PDE transport of the level set function. Tests are presented for both transport as well as two-phase flows, that suggest that this technique is capable of retaining the thin liquid structures that are expected in turbulent atomization of liquids.