Modeling the steady-state temperature field in lava flow levées

The rationale of lava flow deviation is to prevent major damage, and, among the possible techniques, the opening of the flow levées has often been demonstrated to be suitable and reliable. The best way to open the levées in the right point, in order to obtain the required effect, is to produce an explosion in situ, and it is then necessary to map with the highest precision the temperature field inside the levées, in order to design a safe and successful intervention. The levées are formed by lava flows due to their non-Newtonian rheology, where the shear stress is lower than the yield stress. The levées then cool and solidify due to heat loss into the atmosphere. In this work we present analytical solutions of the steady-state heat conduction problem in a levée using the method of conformal mapping for simple geometrical shapes of the levée cross-section (triangular or square). Numerical solutions are obtained with a finite-element code for more complex, realistic geometries.