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a b s t r a c tUsing backstepping design, exponential stabilization of the linearized Saint-Venant-Exner (SVE) model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction, is achieved. The linearized SVE model consists of two rightward convecting transport Partial Differential Equations (PDEs) and one leftward convecting transport PDE. A single boundary input control strategy with actuation located only at the downstream gate is employed. A full state feedback controller is designed which guarantees exponential stability of the desired setpoint of the resulting closed-loop system. Using the reconstruction of the distributed state through a backstepping observer, an output feedback controller is established, resulting in the exponential stability of the closedloop system at the desired setpoint. The proposed state and output feedback controllers can deal with both subcritical and supercritical flow regimes without any restrictive conditions.

This work presents a parallel finite element solver of incompressible two-phase flow targeting large-scale simulations of three-dimensional dynamics in high-throughput microfluidic separation devices. The method relies on a conservative level set formulation for representing the fluid-fluid interface and uses adaptive mesh refinement on forests of octrees. An implicit time stepping with efficient block solvers for the incompressible Navier-Stokes equations discretized with Taylor-Hood and augmented Taylor-Hood finite elements is presented. A matrix-free implementation is used that reduces the solution time for the Navier-Stokes system by a factor of approximately three compared to the best matrix-based algorithms. Scalability of the chosen algorithms up to 32,768 cores and a billion degrees of freedom is shown.