Far-field boundary conditions in channeled lava flow with viscous dissipation

Cooling and dynamics of lava flowing in a rectangular channel driven by the gravity force is numerically modeled. The purpose is to evaluate the thermal process as a function of time involving the liquid lava in contact with the solid boundary that flanks lava. Lava rheology is dependent on temperature and strain rate according to a power law function. The model couples dynamics and thermodynamics inside the lava channel and describes the thermal evolution of the solid boundary enclosing the channel. Numerical tests indicate that the solution of the thermo-dynamical problem is independent of the mesh. The boundary condition at the ground and at the levees is treated assuming a solid boundary around the lava flow across which lava can exchange heat by conduction. A far field thermal boundary condition allows to overcome the assumption of constant temperature or constant heat flow as boundary conditions, providing more realistic results. The effect of viscous heating is evaluated and discussed.