The spatial resolution properties of composite compact finite differencing

Demand for spectral-like spatial routines to resolve fine-scale physics is easily satisfied by compact finite differencing. Commonly, the lower-order multi-parameter families at (and near) non-periodic boundaries are independently tuned to meet or exceed the high-order resolution character of the field stencil. Unfortunately, that approach quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Knowing that each composite template owns three ingredients that define their numerical character, only their formal accuracy and global stability have been properly treated in a coupled fashion. The present work presents a companion means for quantifying the resultant spatial resolution properties. The procedure particularly focuses on the multi-parameter families used to diminish the dispersive and dissipative errors at the non-periodic boundaries. The process introduces a least-squares technique of the target field stencil to optimize the free parameters of the boundary scheme. Application of the optimized templates to both the linear convection and Burgers equations at a fictitious non-periodic boundary showed major reductions of the predictive error.