Ein adaptives Bewegte-Gitter-Verfahren zur Berechnung von Aufschmelz- und Erstarrungsvorgängen

Abstract

Numerical simulations of melting and solidi cation problems is a demanding eld in computational uid dynamics. A moving phase change interface and the temperature dependent thermophysical properties introduce additional non-linearities to the governing equations. Special numerical techniques are needed to perform accurate computations of free boundary problems. A new front tracking method is presented to solve convection-dominated melting and solidi cation problems in arbitrarily formed enclosures. The well known numerical concept of a Control Volume based Finite Element Method is extended to moving boundary problems by an adaptive moving grid model based on unstructured triangular grids. At every sampling instant, the liquid-solid phase interface is resolved explicitly in the numerical grid. To extend the numerical model to phase change problems with phase transition regions between liquid and solid (mushy phases) a two-domain enthalpy-porosity model is also implemented. Local grid adaption algorithms (relaxation, re nement, coarsening) are used to avoid grid distortion due to the moving interfaces. Even in problems involving large scale interface motion or boundary deformation, a continuous high quality grid can be preserved. Additional numerical errors due to highly-distorted elements are also minimised to as far as possible. Furthermore, the use of local grid adaption tools enables dynamical adaption of local grid resolution. During transient calculations local mesh sizes can be adapted on changing physics (e.g. a change in state) to increase computational e ciency. Numerous test calculations are presented to demonstrate the ability of the numerical code. Simulation results are veri ed by comparison with analytical results, benchmark calculations and previous experimental data.