In this paper we are concerned with the numerical study of viscoelastic diphasic flows. We first propose a complete model and give some formal justifications including the case where both or one phase is a non-Newtonian one. Then, we have implemented a numerical method taking into account the lagrangian transport in the resolution of the extra-stress equation of Oldroyd type. We describe this fully-practical method and prove its stability so that one can perform long-time numerical simulations. Several significant tests (channel under shear, filling of tanks, breakup of jets...) illustrate the pertinency of the model and of the numerical method. We show that the results are in accordance with the various qualitative behaviors observed in physical experiments.
Pyroclastic flows are mixtures of volcanic gases and particles that can be very hazardous owing to their fluid‐like behavior. One possible mechanism to explain this behavior is the reduction of particles friction due to the internal gas pore pressure. To verify this hypothesis, we present a numerical model of a granular flow with high initial pore pressure that decreases with time as the gas‐particle mixture propagates. First, we validate the model by reproducing laboratory experiments. Then, the numerical code is applied to pyroclastic flows of Lascar volcano (1993 eruption, Chile). The simulation reproduces the runout and the morphological features of the deposits, with lateral levées, a central channel, and a lobate front. Our results support the hypothesis of the role of gas pore pressure in pyroclastic flows and explain both the fluid‐like behavior of the flows and the formation of lateral levees.
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