These cases typically involve flow with dynamic free surfaces, and often include multiple phases, heat transfer, fluid-structure interaction, or other physics. In this Special Issue of IJCFD we are honoured to present a broad selection of the state of the art of SPH modelling in industrially important applications. SPH is now a mature engineering tool for problems that are challenging for conventional mesh-based CFD. The SPH r Esearch and enginee Ring International Community (SPHERIC, was founded in 2005 to bring together developers and practitioners of SPH in all fields to foster innovation and collaboration. Extensive analysis of the method has been given by Monaghan ( Citation2012), Price ( Citation2012), Violeau ( Citation2012), and Vacondio et al. Since then, there has been sustained growth and innovation both in the mathematics and numerics of SPH and in the diversity and quality of validated engineering applications. Monaghan ( Citation1994) pioneered the extension of SPH to certain engineering problems, with the first application to water waves. The foundational idea of SPH was to replace a classical mesh with Lagrangian particles, interacting through compactly supported kernel functions. These usually involve matter with a dynamic free surface boundary, undergoing rapid changes of scale with complex physics. Smoothed Particle Hydrodynamics was created by Gingold and Monaghan ( Citation1977) and Lucy ( Citation1977) to address the challenges of computational modelling of astrophysical processes.
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