The Effects of the Boundary Stencils on the Field Spatial Resolution When Using Compact Finite Differences

When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at non-periodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the proposed procedure. Application of the couples templates to Burgers equation at the non-periodic boundary showed significant differences in the predictive error.