Verification Of A 2D Finite Element Debris Flow Model Using Bingham And Cross Rheological Formulations
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C. Martinez, F. Miralles-Wilhelm & R. Garcia-Martinez
We propose a vertically-averaged 2D debris flow model based on the non- Newtonian Bingham and Cross rheological formulations. In the Cross model, fluid viscosity changes continuously through the range of shear rates. The 2D model is based on the shallow water equations, where the internal friction losses are implemented using the Cross constitutive relations. The numerical method is based on a four-step, selective lumping, explicit time stepping scheme. We present preliminary tests for one dimensional and two dimensional dam break problems. Model results show very good agreement with experimental data and analytical solutions in one dimensional cases. For the flow early stages, the numerical solution agrees better with the experimental data than with the analytical solution. However, in final stages, the numerical solution predicts that the fluid front advances more rapidly than the analytical solution and measured fluid front. The proposed 2D debris flow model provides very stable results even in the range of very low shear rates, where other discontinuous constitutive relations that use the yield stress may become unstable. Keywords: debris flow, Cross model, Bingham model, yield stress, finite elements.
debris flow, Cross model, Bingham model, yield stress, finite elements.