Laser supported processes can be used to modify the electrical and thermal properties of ceramic substrates locally. These processes are characterised by a strong thermal interaction between the laser beam and the ceramic surface which leads to localised melting. During the dynamic melting process an additive material is injected into the melt pool in order to modify the physical properties. The heat and mass transfer during this dynamic melting and solidification process has been studied numerically in order to identify the dominant process parameters. Simulation tools based on a finite volume method have been developed to describe the heat transfer, fluid flow and the phase change during the melting and solidification of the ceramic. The results of the calculation have been validated against experimental results.