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An Implicit Compact Fourth-order Algorithm for Solving the Shallow-water Equations in Conservation-law Form

Ionel Michael NavonHilarle Alys Riphagen

出版	National Research Institute for Mathematical Sciences, 1979
URL	http://books.google.com.hk/books?id=RHDRtgAACAAJ&hl=&source=gbs_api

註釋

"An alternating-direction implicit finite-difference scheme is developed for solving the nonlinear shallow-water equations in conservation-law form. The algorithm is second-order time accurate, while fourth-order compact differencing is implemented in a spatially factored form. The application of the higher order compact Padé differencing scheme requires only the solution of either block-tridiagonal or cyclic block-tridiagonal coefficient matrices, and thus permits the use of economical block-tridiagonal algorithms. The integral invariants of the shallow-water equations, i.e., mass, total energy and enstrophy, are well conserved during the numerical integration, ensuring that a realistic nonlinear structure is obtained". - Abstract.