Accurate phonon transmission coefficients are essential for controlling heat transport and designing phononic metamaterials. Conventional models for computing transmission coefficient are based on plane-wave solution and spectrum weighting, limiting their ability to capture actual phonon transport dynamics in multi-interface heterostructures. Here we develop an analytical framework that incorporates spatial coherence and validate it against time-domain wave-packet simulations. We show that spatial coherence strongly affects transmission in multi-interface systems, whereas it is negligible for a single interface. The developed framework is robust for various wave-packet profiles and can accurately resolve both transmission coefficient and the wave-packet dynamics in realistic multi-interface heterostructures. Our work provides a robust framework for exploring coherence effects in phonon transport, which may offer guidelines for thermal management and design of phononic metamaterials.

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• Heat transfer
• Phonons
• Interfaces
• Molecular dynamics