A 3D fluid flow and heat transfer can be computed in the part of the global model. A 2D region of the global model meshed structurally in 2D or a group of such regions can be selected and defined as a local 3D computational domain.

In the local 3D domain the cylindrical 3D mesh will be created by a simple rotation of the 2D mesh N times around of the cylindric symmetry axis. The 3D nodes become the same radial and axial coordinates like the origin in 2D. For each 2D node N nodes will be created by different azimuthal angle coordinate.

The differential equations in 3D are discretized according to the same Finite Volume method applied in 2D. Additionally the convective and diffusive fluxes over the azimuthal sides of the 3D control volume are evaluated by means of the finite differences for derivatives with respect to the azimuthal angle.

The 3D execution can be done in the stationary and time-dependent mode, thermally coupled with the global 2D model. The azimuthally averaged instanteneous heat flux in 3D is balanced with the total heat flux computed on the 2D side.

The crystal shape and the shape of the phase interface crystal-melt are assumed to be axisymmetric. The phase tracking procedure is executed in 2D using the azimuthally averaged temperature distribution in the 3D melt region.

The possible applications of the local 3D model for the crystal growth configurations are all methods with cylindrically symmetric melt containers like different modifications of the Czochralski method and the Bridgmann method. A finite tilt angle of the cylindrically symmetric crucible with respect to the vertical direction can also accounted for the Bridgmann method.