Modelling of a highly-viscous, non-isothermal Fluid with free Surface using Model Reduction

Abstract

For model-based control and/or diagnosing purposes it is necessary to determine mathematical models that are sufficiently precise on the one hand, but do not require too much computational effort on the other. In this regard, reduction of a model describing the processing of a highly-viscous, non-isothermal fluid with a free-surface is examined. The behaviour of the fluid is given by a system of partial differential equations containing the two dimensional Navier-Stokes equations and the thermal energy equation. Using perturbation theory it can be shown that the behaviour of the velocity and the temperature can be described sufficiently precise by two simpler submodels. The first submodel is used to calculate the flow dynamics and the second submodel to calculate the thermal behaviour with simultaneous adaptation of the flow dynamics to the current thermal conditions. In addition, the Marker and Cell method is used to determine the temporal development of the free-surface. Finally, the spatial discretisation is done with a curved grid, resulting in a smaller model size than the use of a rectangular grid.