HeatFlow: An open-source implicit finite-difference solver for dynamic thermal transport in metamaterials

Abstract Thermal systems increasingly operate under time-varying conditions, making transient analysis essential alongside steady-state analysis for thermal metamaterials. We introduce HeatFlow , an open-source, implicit, cell-centred finite-difference solver for Fourier and Cattaneo heat transport in structured materials. The code is verified against an analytical heated-bar solution, reproduces established Fourier-regime benchmarks for cloaks, rotators, and concentrators, and is demonstrated on a simplified hemispherical shield with isotropic conductivity contrasts. We also connect the solver to published non-Fourier metamaterial disc designs. These examples establish HeatFlow as a practical platform for thermal-metamaterial design and a foundation for investigating transient non-Fourier thermal effects.