Adaptivity for finite volume on unstructured triangular meshes: a study of thermal injury in teeth

This paper presents a numerical study of thermal injury in teeth, caused both by convective heating, due to drinking of hot beverage and mastication of foods, and by laser irradiation in dental treatment. The numerical study employs an adaptive finite volume method on unstructured triangular meshes to solve the governing equations. An adaptive time stepping methodology was also used in order to control the solution error. Adaptive methodologies are adequate to solve such problems since steep gradients will develop at specific locations in the domain of study. The convective heating results were compared to experimental data available in the literature. Laser treatment results are in agreement to the temperature increasing observed in literature. The simulation results demonstrate that both the error estimate and adaptive methodology herein proposed are suitable and reliable for the controlled solution of parabolic problems