科研之友
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摘要
A Roe-type decomposition for a system of equations governing onshore/offshore wave transformation in coastal waters is derived. The equation set approximated pertains to coastal waters prior to wave breaking, and is based on depth-averaging and time-averaging of the Euler equations. The equations are those used in many commercial codes for simulation of wave height and wave-averaged currents. This novel approach uses a combination of some standard Roe averages, together with physical reasoning and power series expansions to derive a Roe-averaged Jacobian (with real, linearly independent eigenvectors) and ensures conservation, and thereby effects the decomposition. It is shown that the resulting derived Roe-averaged quantities are accurate to a high degree, by comparing them with their analytical equivalents for a wide range of nondimensional water depths and slopes likely to be encountered in coastal problems. Numerical tests of time-invariant wave height transformation and wave group propagation are undertaken; these indicate good performance of the scheme in practice.
- 出版日期2012-7-10
