Implicit smoothed particle hydrodynamics for nonlinear heat transfer in rubberized concrete: Validation and comparison with the generalized finite difference method

Abstract

This study presents an implicit Smoothed Particle Hydrodynamics (SPH) framework for the simulation of transient heat conduction in rubberized concrete with temperature-dependent thermal properties.The proposed formulation combines an unconditionally stable implicit time integration with a matrix-based SPH discretization, enabling robust treatment of nonlinear material behavior. In addition, an efficient linked-list neighbor-search strategy is implemented to reduce the computational complexity of particle interactions from quadratic to linear scaling with respect to the number of particles.The accuracy of the method is first verified against the analytical solution of a two-dimensional heat conduction problem with constant properties, showing excellent agreement and confirming the consistency of the formulation. The approach is then extended to nonlinear thermal problems involving temperature-dependent conductivity, density, and heat capacity, representative of heterogeneous cementitious materials. A detailed comparison with the Generalized Finite Difference Method (GFDM), performed under identical discretization and boundary conditions, demonstrates that both approaches achieve similar levels of accuracy. However, the proposed SPH framework remains computationally efficient due to the optimized neighbor-search procedure and the implicit formulation.These results demonstrate that the proposed SPH approach provides a robust and flexible alternative for modeling nonlinear heat transfer in heterogeneous materials, with potential applicability to problems involving evolving geometries and coupled thermo-mechanical processes.