Fast simulation of viscous lava flow using Green's functions as a smoothing kernel

We present a novel approach to simulate large-scale lava flow in real-time. We use a depth-averaged model from numerical vulcanology to simplify the problem to 2.5D using a single layer of particle with thickness. Yet, lava flow simulation is challenging due to its strong viscosity which introduces computational instabilities. We solve the associated partial differential equations with approximated Green's functions and observe that this solution acts as a smoothing kernel. We use this kernel to diffuse the velocity based on Smoothed Particle Hydrodynamics. This yields a representation of the velocity that implicitly accounts for horizontal viscosity which is otherwise neglected in standard depth-average models. We demonstrate that our method efficiently simulates large-scale lava flows in real-time.