Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure

Optimal control of an advection-dominated catalytic fixed-bed reactor with catalyst deactivation

The paper focuses on the linear-quadratic control problem for a time-varying partial differential equation model of a catalytic fixed-bed reactor. The classical Riccati equation approach, for time-varying infinite-dimensional systems, is extended to cover the two-time scale property of the fixed-bed reactor. Dynamical properties of the linearized model are analyzed using the concept of evolution systems. An optimal LQ-feedback is computed via the solution of a matrix Riccati partial differential equation. Numerical simulations are performed to evaluate the closed loop performance of the designed controller on the fixed-bed reactor. The performance of the proposed controller is compared to performance of an infinite dimensional controller formulated by ignoring the catalyst deactivation. Simulation results show that the performance of the proposed controller is better compared to the controller ignoring the catalyst deactivation when the deactivation time is close to the resident time of the reactor.Scopu

cardiac pump

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