Computational Algorithm

CAA phenomena are, by definition, time-dependent. Thus, a time marching algo­rithm will naturally be required. In previous chapters, the 7-point dispersion-relation­preserving (DRP) scheme has been shown to have good dispersion and dissipative properties. It provides good resolution when using 7 or more mesh points per wave­length. In some situations, however, in order to meet the 7 mesh points per wave­length requirement, it will result in the use of an extremely small mesh. This is not desirable. Under this circumstance, one may use a larger stencil DRP scheme in just the part of the computational domain where the extra resolution is required. The 15-point stencil DRP scheme has a good resolution when using as few as 3.5 mesh points per wavelength. So it is a good strategy to use the 15-point stencil DRP scheme in the subdomain with very stringent resolution requirement and then transition to a 7-point stencil DRP scheme outside this subdomain.