11/30/2022 0 Comments Savage xr evolution![]() ![]() For the correct and reliable descriptions of flow behaviour and the numerical stability, we need the exact descriptions of eigenvalues of the system representing the dynamics of the mass flows. As the physical mathematical model, we consider the general two-phase debris flow equations developed by Pudasaini (2012) as a mixture of viscous fluid and solid particles. The model, which includes several important physical aspects of the real two-phase mass flows, reveals strong interactions between the phases, is written as a set of a well-structured, highly non-linear, hyperbolic-parabolic partial differential equations. Based on this model, here, we analytically construct several novel and general exact eigenvalues for both the solid- and fluid-phases. We call these phase-eigenvalues the solid- and fluid-phase-eigenvalues. ![]() Associated phase-Froudenumbers and phase-wave-speeds are also defined and determined. Enhanced simulations for two-phase mass flows down an inclined channel have been carried out by applying these exact eigenvalues together with the high-resolution TVD-NOC simulation schemes and computational codes. This resulted in an appropriate determination of the enhanced flow dynamical quantities, including the evolution of the solid- and fluid-phase, fluid volume fraction, and the total debris height. Results are also compared by applying the derived phase-eigenvalues that incorporate the strong phase-interactions in the two-phase debris movements against the simple and classical solid-only, and fluid-only eigenvalues without the phase interactions. Simulation results clearly indicate the importance of the new phase-eigenvalues and strongly support for the implementation of the complete phase-eigenvalues for the enhanced and appropriate descriptions of real two-phase landslides, avalanches, debris flows, particle-laden flows and flash-floods. This work presents a high-order element-based numerical simulation of an experimental granular avalanche, in order to assess the potential of these spectral techniques to handle geophysical conservation laws. The spatial discretization of these equations was developed via the spectral multidomain penalty method (SMPM). ![]()
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