Combined prefactored compact schemes for first- and second-order derivatives: conceptual derivation
This provides a method to improve accuracy for numerical differentiation in computational fluid dynamics or similar fields without increasing computational cost per grid point.
The paper derives combined prefactored compact schemes that increase the order of accuracy of original prefactored compact schemes from sixth to eighth or from eighth to tenth without expanding the stencil width.
The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the original schemes can be increased from sixth to eight, or from eight to tenth (depending on the order of the original scheme), while the number of grid points in the stencil is kept the same. Here, we only frame the conceptual derivation of the schemes, leading to a closed set of equations for the weights.