Thermal simulation in multiphase incompressible flows using coupled meshfree and particle level set methods

A particle-based numerical solver is presented, applicable to the simulation of heat transfer in multiphase immiscible flows including surface tension. In the context of meshfree methods, the Laplacian operator is recognized as the most numerically challenging ingredient of the heat equation. The well-known difficulty of approximating higher-order spatial derivatives with meshfree methods is herein addressed by adopting two advanced schemes in order to ensure second-order accuracy. In addition, a Lagrangian particle level set method with second-order reinitializationis introduced, for the first time in thermal simulations, to capture the location of the interface, i.e., moving and/or deformable boundaries of the continuum at each time-step. This leads to a more conservative solution, alleviating the mass loss during the simulation. Furthermore, a narrow band of the exterior geometric particles is exploited to form physical ghost particles to enforce the required boundary conditions. This novel approach ensures solver performance without the necessity of defining extra dummy particles for treating boundary conditions in meshfree simulations. Three benchmark problems are considered for evaluating the performance of the proposed solver against a reference analysis performed in COMSOL Multiphysics®.