We propose a new kind of compact difference scheme for the computation of the first and second derivatives in the simulation of high-Reynolds number turbulent flows. The scheme combines and truncates the pseudospectral representation of derivative for convergence acceleration. Comparison of the wave resolution property with available optimized compact schemes minimizing the prescribed wave resolution error reveals our scheme's superiority for the same size of stencils without introducing optimization parameters. An accompanying boundary scheme is also proposed with the stability analysis. The proposed scheme is tested for the evaluation of derivatives of a function that decays very slowly in the wavenumber space, and for the simulation of three-dimensional isotropic turbulence.
Bibliographical noteFunding Information:
We are grateful to the anonymous referees for very fruitful comments. We acknowledge the support by the Korea Research Foundation through Grant KRF-99-003-E00014.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics