Shall 4: An Implicit Compact Fourth-Order Fortran Program for Solving the Shallow-Water Equations in Conservation Law Form

摘要

A FORTRAN 4 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 o the finite element method and has a smaller truncation error than the usual fourth order schemes. The integral invariants of the shallow water equations were calculated at each time step and were found 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.