Abstract
We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e. the convective operator is represented by a skew-symmetric matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. Such a symmetry-preserving discretization of the NavierStokes equations is stable on any grid, and conserves the total mass, momentum and kinetic energy (when the physical dissipation is turned off). Its accuracy is tested for a turbulent channel flow at Re=5,600 (based on the channel width and the mean bulk velocity) by comparing the results to those of physical experiments and previous numerical studies. This comparison shows that with a fourth-order, symmetry-preserving method a 64 x 64 x 32 grid suffices to perform an accurate direct numerical simulation
Keywords
- Direct Numerical Simulation
- Coefficient Matrix
- Skin Friction Coefficient
- Turbulent Channel Flow
- Diffusive Operator
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Verstappen, R.W.C.P., Veldman, A.E.P. (2002). Symmetry-Preserving Discretization of Turbulent Channel Flow. In: Breuer, M., Durst, F., Zenger, C. (eds) High Performance Scientific And Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55919-8_12
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DOI: https://doi.org/10.1007/978-3-642-55919-8_12
Publisher Name: Springer, Berlin, Heidelberg
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