Prefactored Small-Stencil Compact Schemes

A new type of prefactored compact schemes is presented that obtains high-order accuracy while using a very small stencil size. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than the existing compact schemes. Results are shown for linear and nonlinear 1-D benchmark problems and a 2-D linear benchmark problem. Boundary stencils for both exterior and interior multiblock boundaries are given, and boundary condition specification is described and demonstrated.