Simulating thermal convection with meshless methods: Lagrangian vs Eulerian models
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The present study introduces the $\delta^\star$-SPH model which is a quasi-Lagrangian smoothed particle hydrodynamics (SPH) model for the simulation of multiphase thermal convection problems. Building upon the framework developed in \cite{huang2025jcp}, the model is extended to account for thermal effects. Two alternative strategies for the enforcement of thermal boundary conditions are investigated and systematically compared. The accuracy and convergence properties of the proposed SPH formulation are assessed through a set of benchmark problems, including both single-phase and multiphase configurations. High-fidelity reference solutions are provided by high-order polyharmonic splines-radial basis function (PHS-RBF) \cite{bartwal2025cf} and generalized finite difference method (GFDM) \cite{suchde2019jcp} based meshless frameworks. In addition, the study offers a comparative assessment of Lagrangian and Eulerian formulations, highlighting their respective advantages and limitations in terms of accuracy, robustness, and suitability for thermal convection problems. The results demonstrate that the proposed SPH model is capable of accurately reproducing thermal convection phenomena across a range of test cases.
