Verification Of A 2D Finite Element Debris Flow
Model Using Bingham And Cross Rheological
Formulations
Author(s)
C. Martinez, F. Miralles-Wilhelm & R. Garcia-Martinez
Abstract
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.
Keywords
debris flow, Cross model, Bingham model, yield stress, finite
elements.
Related Book
Other papers in this volume
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