A Filter-Matrix Lattice-Boltzmann Methodology for Convective Melting and Solidification

We present a methodology for simulating melting and solidification within a lattice Boltzmann framework utilizing filter-matrix collision operators. This approach integrates a source-based enthalpy method for phase change and an immersed boundary scheme to enforce the no-slip condition at the evolving phase interface. The proposed methodology demonstrates excellent agreement with benchmark cases, including the Stefan problem and the analytical model for transient freezing in channel flow between two isothermally cooled parallel plates. Further validation is performed on two more complex scenarios: Ice layer formation in a cavity driven by natural convection and channel flow with a constant flux of heat removal, both of which show strong agreement with reference data. Given the enhanced stability of filter-matrix collision operators, future work could extend this approach to turbulent melting and solidification simulations.