Dr.-Ing. Aleksei Sokolov

Technische Universität Berlin

Applications of VHE and BTE for the description of Raman Optothermal Experiment

Heat transport in dielectric crystals is governed by the Boltzmann Transport Equation (BTE), whose applicability range spans multiple length scales and temperatures. Yet its practical use remains limited, as the solution of the BTE typically requires Monte Carlo solvers that become prohibitively expensive, particularly in complex geometries.

We introduce two alternative strategies that address these limitations. The first is a spectral decomposition of the BTE, in which the full transport spectrum is precomputed once and subsequently enables rapid evaluation of thermal transients for arbitrary initial conditions in the infinite domains. The second is based on recently formulated viscous heat equations (VHE) which allow direct finite element discretization. We develop and implement a FEM solver for VHE in FEniCS capable of capturing non-Fourier thermal transport with admissible computational load.

We demonstrate both approaches in comparison with time- and space-resolved Raman thermometry, highlighting their ability to reproduce experimental signatures of anomalous heat conduction.