Moving boundary methods for the simulation of two-fluid and sediment-fluid interactions

Abstract

One challenging category of problems in flow computation is the modeling of moving boundaries and interfaces. There are different techniques to model such problems: interface tracking and interface capturing methods. In this work, we study two methods of modeling moving boundaries and interfaces in CFD problems. This choice is made considering the type of problem under consideration: two-fluid and sediment-fluid interactions. The first one is related to the interaction between two fluids with different properties, like water and air, and the second one is about the interaction between a fluid and a sediment bottom that deforms as the flow evolves. Therefore, we implement the convected level-set method to model two-fluid problems. The mathematical model results from the Navier-Stokes equations treated with the Residual Based Variational Multiscale formulation, together with the convected level-set method, used to track the interfaces between the different fluids. Here, we introduce a new truncated signed distance function to get a smooth truncation far from the interface. On the other hand, to model sedimentfluid interaction, we present a full approach within the Arbitrary Lagrangian-Eulerian framework with mesh adaptivity. The Navier-Stokes equations are combined with an advection-diffusion equation for suspended sediments. The morphological changes are calculated by empirical models used to represent the entrainment rate as well as the bedload transport. The displacements, and consequently, the interface motion, are applied as mesh movement. We introduce a new smoothing technique called upwind sand-slide, in which we adjust the slope angle considering the flow direction. We validate the algorithm with test cases where experimental and numerical data are available. Finally, the results are discussed and analyzed.