The hole-filling method and multiscale algorithm for the heat transfer performance of periodic porous materials

• A multiscale analysis and computation based on hole-filling method is proposed.
• Transient heat transfer problem of periodic porous materials is considered.
• Proof of the limiting process as the parameters of the weak phase go to zero is derived.
• Some numerical results are given in detail to validate the multiscale method developed.

In this paper, we consider the transient heat transfer problem with rapidly oscillating coefficients in periodic porous materials. The hole-filling method through filling all holes with a very compliant material is investigated, and as the thermal conductivity parameters of the weak phase go to zero, the proof of the limiting process is derived in detail. Then, the multiscale analysis and computations based on the hole-filling method for the associated multiphase problem in a domain without holes are proposed. Finally, some numerical results are given, which show a good agreement and verify the feasibility of the hole-filling method.