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A finite volume method for geometries parameterized by Non-Uniform Rational B-Splines (NURBS) is proposed. Since the computational grid is inherently defined by the knot vectors of the NURBS parameterization, the mesh generation step simplifies here greatly and furthermore curved boundaries are resolved exactly. Based on the incompressible Navier-Stokes equations, the main steps of the discretization are presented, with emphasis on the preservation of geometrical and physical properties. Moreover, the method is combined with a structural solver based on isogeometric finite elements in a partitioned fluid-structure interaction coupling algorithm that features a gap-free and non-overlapping interface even in the case of non-matching grids.

This paper presents efficient numerical methods—the “inverse modeling” method and the adaptive finite element method—for optimizing the heat transport as well as for investigating the heat and mass transport under the influence of convection during crystal growth, especially near the liquid/solid interface. These methods have been applied to industrial Bridgman-furnaces for the growth of 65–75 mm diameter (Cd,Zn)Te crystals.

S-doped InP crystals were grown from an In-solution in a THM arrangement during the EURECA-1 mission using the automatic mirror furnace (AMF) under microgravity conditions. The InP-crystals showed growth rate oscillations in the range of 0.8–2.0 μm/min with a period of 45 min, which is half the time of an orbit of the EURECA-1 satellite. The fluid dynamic conditions during this experiment are modelled using a 3D model with the commercial software FIDAP. The time-dependent simulation, considering thermal as well as solutal buoyancy effects, indicates a weak laminar flow in this material system. Due to the fixed attitude of the satellite with respect to the sun the residual gravity vector rotates relative to the sample axis. This rotation results in a significant change of the residual convection level. Its maximum is obtained, when the gravity is parallel to the growth interface (two times during each orbit). Due to a high Schmidt number Sc≈25 a time-dependent influence of the convection on the concentration field can also be observed.

The use of do-loops in connection with variables for the FIDAP mesh generation is demonstrated. Special focus is drawn on the advantage of labeling objects explicitly especially for more complicated meshes. These concepts are illustrated with the mesh generation for a three zone resistance furnace.

A numerical modelling of the heat transport in a three-zone resistance furnace has been performed.The results of the calculations agree very well with experimentally obtained temperature profiles. A strong dependence of the calculated temperature field on the thermal conductivity of the furnace material is observed and can be explained by nonisotropic effects like inhomogeneities in the insulation.The simulations can also predict the influence of modifications in the furnace set-up like an additional electromagnet instead of an outer insulation layer. Further, the computer model is used to reveal the influence of different positions of a growth ampoule. The temperature field in the ampoule shows a decrease of the temperature gradients at the phase boundary at the end of the growth process and a change of the interface shape from concave to convex.