Time-Adaptive Fully Coupled Parallel Simulation of Sand Dune Morphodynamics
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In this work, we present a fully coupled multiphase mixture model for sand dune morphodynamics, in which sand and air are represented within a single volume-averaged continuum. The formulation couples an approximate Navier--Stokes-like mixture momentum equation and an incompressibility constraint with a convection--diffusion equation, enabling the description of the coupled evolution of airflow, sediment transport, and the sand--air interface. The diffusive contribution incorporates a degenerate parabolic sliding model, adapted to the volume-fraction formulation to account for gravity-driven avalanching when the local interface slope exceeds a prescribed critical value. The model is assessed through two-dimensional numerical experiments involving sedimentation and avalanching, followed by airflow-driven dune evolution under two reference wind velocities. The results demonstrate that the adaptive linearly implicit scheme provides improved computational efficiency compared with fixed-step implicit Euler integration over the same physical time interval, while accurately capturing the relevant morphodynamics processes. computational fluid dynamics, avalanching, sand-dune dynamics, linearly implicit method, finite volume method
