Introduction

CrysMAS is a program for global numerical simulation of Crystal growth processes in complex furnaces with axial or translational symmetry. It is based on the Finite Volume method and an Unstructured mesh. Recently numerical methods for structured mesh were implemented and the computation on the hybrid numerical mesh was enabled. The simulation provides information for making predictions about physical quantities, so called variables, in a complex system and for controlling the crystal growth process.

Global simulation has to consider all relevant physical phenomena influencing the variables investigated. Temperature is the most important variable and the basis for computing other variables like heat flux, flow velocity and von Mises Stress.

CrysMAS allows to compute simulations in both directions:

CrysMAS is able to perform stationary and time-dependent simulations for furnaces heated by resistance as well as by inductive heaters. The program can control an arbitrary number of heaters and also in case of inverse simulation an arbitrary number of control points.

The program CrysMAS is a product of merging together of two different algorithm groups. The first group operates on the unstructured triangle mesh while the second group is specialized on the block-structured mesh. First the program CrysVUn++ was established as a Finite Volume based thermal simulation tool utilizing algorithms on the unstructured mesh. The inverse modeling and thermal stress calculation was also supported. Recently the code was further developed towards the multi-physics application. The fluid flow, inductive heating, different kinds of treated electromagnetic fields, alloy solidification etc. were added. The core of the code was consequently changed and the second group of algorithms on the block-structured mesh was incorporated. Now computations can be executed using a combination of the unstructured and structured numerical meshes or on so-called hybrid mesh in order to enhance the computational efficiency. A new enhancement of the code is the local 3D modeling of the fluid flow fully coupled with the global 2D thermal model. The time dependent and 3D fluid flow which occurs in the axisymmetric crucibles in such configurations as Czochralski or tilted Bridgmann can be modeled now within the framework of the global thermal exchange. The 3D fluid flow is treated by means of the direct numerical solution of the Navier-Stokes and enthalpy transport equations in cylindrical coordinates. For each region of the computational domain either the 2D or 3D treatment may be selected. The thermal coupling between the 3D and 2D part of the model is automatically accomplished.

Basic knowledge in thermal analysis and mathematical simulation is prerequisite. Specific knowledge needed for running CrysMAS will be imparted in this documentation.