swMATH ID: 7
Software Authors: Navon, I.M.; Riphagen, H.A.
Description: SHALL4 - an implicit compact fourth-order Fortran program for solving the shallow-water equations in conservation-law form. A FORTRAN IV computer program is documented implementing a compact fourth-order accurate finite difference scheme in a spatially factored form, for solving the nonlinear shallow-water equations on a limited domain. In contrast to the usual fourth-order schemes this compact fourth-order scheme requires the solution of only either block-tridiagonal or cyclic block-tridiagonal coefficient matrices. Moreover this compact fourth-order scheme is related to the finite-element method and has a smaller truncation error than the usual fourth-order schemes. The integral invariants of the shallow-water equations are calculated at each time-step and were determined to be well conserved during the numerical integration, ensuring that a realistic nonlinear structure is obtained. A Schumann-Wallington low-pass filtering procedure was incorporated in the program to overcome the increased aliasing due to the higher accuracy method. A third-order boundary condition is imposed, preserving the overall fourth-order convergence rate of the interior approximation.
Homepage: http://people.sc.fsu.edu/~inavon/pubs1/exshall4.pdf
Keywords: implicit compact fourth-order Fortran program; shallow-water equations; conservation-law form
Related Software: FDL3DI
Cited in: 4 Publications

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