2018/05/03 by Ágnes Rieth, Rieth, A., Róbert Kovács +3 · 1 citation
Engineering · Materials Science · Mathematics · #FOS: Physical sciences #Numerical methods in inverse problems #Statistical Mechanics (cond-mat.stat-mech) #Thermal properties of materials #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1805.01108
openalex publication_date 2018/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are various situations where the classical Fourier's law for heat conduction is not applicable, such as heat conduction in heterogeneous materials or for modeling low-temperature phenomena. In such cases, heat flux is not directly proportional to temperature gradient, hence, the role -- and both the analytical and numerical treatment -- of boundary conditions becomes nontrivial. Here, we address this question for finite difference numerics via a shifted field approach. Based on this ground,implicit schemes are presented and compared to each other for the Guyer--Krumhansl generalized heat conduction equation, which successfully describes numerous beyond-Fourier experimental findings. The results are validated by an analytical solution, and are contrasted to finite element method outcomes obtained by COMSOL.