A Characteristic-mixed Finite Element Simulation For Two Dimensional Sediment Transport Model

Current and silt sedimentation model plays an important role for quantitative pre-diction of the sediment movements and the evolution of the river bed. It is commonlyused in simulating the formation and development of the delta, the expansion of the sed-imentation area, the river channel change caused by the transport and deposition of thesilts and sediments. The intensive study of this problem will help people to understandthe flow and sediment of river morphology more clearly, and it also has positive signif-icance for the construction and reinforcement of sand control, flood control and dam.Since the model is hard to find its exact solution due to its complexity, its numericalsimulation has aroused great concern of hydrodynamic engineers and numerical analysts.In this paper, we describe the two-dimensional current and silt sedimentation trans-port process by a mathematical model: which contains the flow continuity equation, thewater movement equation, the sediment continuity equation, the river bed deformationequation, involving water depth H, flow velocity U, silt concentration S and the bedelevation Zbrespectively.In practical applications, people pay more attention to the flow velocity U and thesilt concentration S. However, the flow velocity U appears in the sediment continuityequation, and the fluxes S is embodied in the water movement equation. So the highprecision calculation for U and S depends heavily on high precision of S. Hence, thenumerical discrete scheme should recognize both S and S with high accuracy simulta-neously. Finite element method can often approximate the unknown function with high precision, but cannot guarantee approaching its gradient with high accuracy at the sametime. However, the mixed finite element method has the advantages of high precision forthe unknown function and its gradient simultaneously. We also note that the convectionterms existing in the model will result in non-physical oscillations and the numericaldispersion on the flow front. Therefore, we consider the characteristic to improve thestability of the discrete procedure.Based on the above considerations, we use the characteristic finite element methodto discrete the flow continuity equation and the water movement equation, and the char-acteristic mixed finite element method to discrete the sediment continuity equation re-spectively, which constitute the characteristic mixed finite element discrete procedure.We give the convergent analysis of the discrete scheme with the inductive hypothe-ses on H, U and S and get the suboptimal L2error estimation. Meanwhile, we also provethat the numerical H has positive lower bound by the hypotheses. The numerical testsverify the theoretical finds.