Summary
A fourth-order Hermitian, or compact scheme has been implemented into the production programs on both sides of the french-german cooperation. On the french side the numerical scheme is applied in its equidistant form on a transformed equidistant grid which gives the desired non-equidistant grid in the physical space. On the german side the fourth-order scheme has been formulated directly for a non-equidistant and staggered grid. The significant improvements in phase error and amplitude error behaviour of the higher-order scheme in comparison to the second-order central scheme is demonstrated in solving simpler test problems and in addition, very complex flow problems such as the non-equilibrium turbulent channel flow and the transitional or fully turbulent backward-facing step flow. The selected complex flow problems are solved by DNS for Re = 3000 and by LES for Re = 13800. The results from LES of periodically forced turbulent channel flow (with hysteresis effects) indicate the necessity of using improved subgrid scale models.
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Meri, A., Wengle, H., Dejoan, A., Védy, E., Schiestel, R. (1998). Applications of a 4th-Order Hermitian Scheme for Non-Equidistant Grids to LES and DNS of Incompressible Fluid Flow. In: Hirschel, E.H. (eds) Numerical Flow Simulation I. Notes on Numerical Fluid Mechanics (NNFM), vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44437-4_19
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DOI: https://doi.org/10.1007/978-3-540-44437-4_19
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