Session Cb - Turbulence Simulation.
ORAL session, Sunday, November 23
302, Moscone Center
We present a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric, and may be considered a more general version of the standard compact (Padé) schemes. They are different from the standard Padé schemes, in that the first and second derivatives are evaluated simultaneously. For the same stencil width, the proposed schemes are two orders higher in accuracy, and have significantly better
spectral representation. Eigenvalue analysis, and numerical solutions of the one-dimensional wave equation are used to demonstrate the numerical stability of the schemes.
The computational cost of computing both derivatives is assessed, and shown to be essentially the same as the standard Padé schemes. The proposed schemes appear to be attractive alternatives to the standard Padé schemes for computations of the Navier Stokes equations.