A Second Order Time Homogenized Model for Sediment Transport

A multiscale method for the hyperbolic systems governing sediment transport in a subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first derive a zeroth order homogenized model and then propose a first order correction. It is revealed that the first order correction for hyperbolic systems has to be applied on the characteristic speed of slow variables in a one dimensional case. In a two dimensional case, besides the characteristic speed, the source term is also corrected. We develop a second order numerical scheme following the framework of heterogeneous multiscale method. The numerical results in both one and two dimensional cases demonstrate the effectiveness and efficiency of our method.

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