A multi-horizon peridynamics for coupled fluid flow and heat transfer

This paper presents a peridynamics-based computational approach for modelling coupled fluid flow and heat transfer problems. A new thermo-hydrodynamic peridynamics model is formulated with the semi-Lagrangian scheme and non-local operators. To enhance accuracy and numerical stability, a multi-horizon scheme is developed to introduce distinct horizons for the flow field and thermal field. The multi-horizon scheme helps to capture the convective zone and complex thermal flow pattern while effectively mitigating possible oscillations in temperature. We validate the computational approach using benchmarks and numerical examples including heat conduction, natural convection in a closed cavity, and Rayleigh–Bénard convection cells. The results demonstrate that the proposed method can accurately capture typical thermal flow behaviours and complex convective patterns. This work offers a new foundation for future development of a unified peridynamics framework for robust, comprehensive multi-physics analysis of thermal fluid–solid interaction problems with complex evolving discontinuities in solids.