A novel numerical method for simulating a droplet in a Leidenfrost state on soft substrates

This work presents a numerical framework for three-phase systems (liquid, gas, visco-elastic solid) using an extended discontinuous Galerkin (XDG) and level-set method. It simulates complex fluid-structure interactions with heat and mass transfer, maintaining strictly sharp phase interfaces without artificial smoothing. After verifying optimal convergence via a fluid-solid Taylor-Couette benchmark, the framework is applied to the Leidenfrost effect. While existing studies typically assume rigid solid surfaces, we investigate deformations induced by localized vapor pressure on soft substrates. We validate quasi-static droplet shapes against existing rigid solid models and derive a novel analytical extension for soft substrates using a Winkler foundation model. Our simulations demonstrate excellent agreement with this new analytical solution. Finally, the framework's robustness is demonstrated by simulating a Leidenfrost droplet sliding down an inclined soft substrate, successfully capturing asymmetric droplet shape, substrate deformation and localized interfacial waves.