A Relaxation Method for Modeling Two-Phase Shallow Granular Flows
Abstract
We present a relaxation approach for the numerical solution of a
depth-averaged two-phase model describing the flow of a shallow layer of a
mixture of solid granular material and fluid. A relaxation model is formulated
by introducing auxiliary variables that replace the momenta in the spatial
gradients of the original system. These new variables are governed by linear
equations with coefficients that determine the eigenvalues of the relaxation
model. The proposed relaxation strategy results in the definition of a particular
approximate Riemann solver for the original model equations. Compared to
a Roe-type Riemann solver that we have proposed in previous work, the new
solver has the advantage of a certain degree of freedom in the specification
of the wave speeds through the choice of the relaxation parameters. This
flexibility can be exploited to obtain a more robust method than the Roe type
one in the treatment of wet/dry fronts. Some numerical experiments are
presented to show the effectiveness of the proposed approach.