A Second Order Time Homogenized Model for Sediment Transport

A multiscale method for the hyperbolic systems governing sedimenttransport in a subcritical case is developed. The scale separation ofthis problem is due to the fact that the sediment transport is muchslower than flow velocity. We first derive a zeroth orderhomogenized model and then propose a first order correction. It isrevealed that the first order correction for hyperbolic systems hasto be applied on the characteristic speed of slow variables in a onedimensional case. In a two dimensional case, besides thecharacteristic speed, the source term is also corrected. We developa second order numerical scheme following the framework ofheterogeneous multiscale method. The numerical results in both oneand two dimensional cases demonstrate the effectiveness andefficiency of our method.