A GPU-based 2D viscous flow model with variable density and heat exchange

Abstract

Numerical simulation of unsteady viscous flow over variable topography under the influence of temperature changes is a challenge. In order to apply the model to large domains with complex topography, it becomes mandatory to reduce the model complexity from 3D to 2D by depth averaging the equations and to apply massive parallelization techniques for an efficient simulation. The depth averaged mass continuity, momentum and internal energy equations, combined with suitable friction laws, can be used for this type of flows. Variations in temperature can be accounted for from internal energy changes with density changing accordingly. The resulting system is solved using a finite volume technique on unstructured triangular grids well suited for problems over variable topography. A generic model applicable to a wide range of viscous fluids and validated with synthetic cases is presented to evaluate the performance of the numerical solution in presence of both external thermal forcing functions and discontinuous initial conditions. Finally, the model is applied to a realistic application and calibration to a particular case of lava flow taking into consideration variable density, viscosity and yield stress with temperature . A heat transfer with the air is included to consider the lava cooling. The numerical results of the lava front advance are compared to the Copernicus satellite observations at different dates. The efficiency of the GPU implementation allows to simulate a 11 day event in less than 1.7 h of simulation.