Compact spatial differencing and subiteration time marching in the PARC code

Compact finite differencing is implemented in the PARC code. It is currently used in the evaluation of the grid metrics, the convective terms, and the artificial dissipation. Compact differencing is used to bring the convective terms from second-order to fourth-order accuracy. In addition, compact differencing is used to take the artificial dissipation from the fourth to the sixth order. Second-order implicit time marching is introduced in the PARC code by a subiteration procedure. Implicit time marching allows much greater time steps to be used as compared to an explicit scheme. Several test cases are presented to demonstrate the effect of these modifications on accuracy and CPU time. Test cases include the Karman vortex street behind a cylinder in crossflow, convection of an inviscid vortex for which an analytical solution is known, and inviscid flow over a leading edge. In addition, an application to 3D unsteady flow about a leading edge with heat transfer was calculated. (Author)

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