|Author:||Fung, Yat-fu Wilson|
|Title:||An efficient semi-implicit finite element scheme for two-dimensional moving boundary tidal flow problems|
|Subject:||Fluid dynamics -- Mathematical models|
Hong Kong Polytechnic -- Dissertations
|Department:||Department of Civil and Structural Engineering|
|Pages:||1 v. (various pagings) : ill. ; 30 cm|
|Abstract:||The usefulness of the semi-implicit finite element scheme for two-dimensional tidal flow computation has been demonstrated in Chen and Li (1990). In that scheme, each term of the governing equations, rather than each dependent variable, is expanded in terms of the unknown nodal values. Simpson's rule is used for numerical integration to make the mass matrix diagonal. The friction terms are represented semi-implicitly to improve stability. In addition, the inclusion of the eddy viscosity terms in the governing equations controls numerical noise and the time-stepping scheme is second-order accurate. But the scheme can only be applied to problems with fixed boundaries. In this report, the scheme is further extended to moving boundary problems. The treatment of the moving boundary is similar to the flooding and drying test scheme adopted by Falconer and Chen and two of their one-dimensional numerical examples are employed to collate with the result computed from our scheme. A simple two-dimensional test problem is also used to further validate the present scheme. A common source of numerical difficulty of numerical models is the presence of artificial, short wavelength spatial oscillations. The methods that have been employed to suppress these spurious oscillations include excess bottom friction (Brebbia and Partridge), use of eddy viscosity terms (Wang, Neves) and time discretization over two time levels (Kinnmark and Gray). The problem is more serious in moving boundary problems. In order to control the computational noise, every nodal values fi is smoothed into a value fi* at each time step by the influence of its four neighbouring nodes : fi*=帢fi+(1-帢)(4峉j=1 ljfj)/4峉j-1 lj where lj is the reciprocal of the distance between node i and node j. Values of 帢 vary with the numerical experiments.|
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