Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

Abstract

This paper concerns the accuracy of several high-resolution and high-order finite volume schemes in Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. The main objective is to investigate the properties of numerical schemes, originally designed for compressible flows, in low Mach compressible, near-wall turbulent flows. Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated. The performance of the schemes has been assessed against incompressible Direct Numerical Simulations. Detailed comparisons of the velocity profiles, turbulent shear stresses and higherorder turbulent statistics reveal that the low Mach correction can significantly reduce the numerical dissipation of the methods in low Mach boundary layer flows. The effects of the low Mach correction has more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes. The ninth-order Weighted Essentially Non-Oscillatory scheme is the least dissipative scheme and it is shown that the implementation of the low Mach correction in conjunction with this scheme has a significant anti-dissipative effect that adversely affects the accuracy. Finally, the computational cost required for obtaining the improved accuracy using increasingly higher order schemes is also discussed.

Near Wall Behavior of Implicit Large Eddy Simulations

“…This essentially involves an additional numerical re-construction step of the velocity vector via a progressive central differencing of the velocity components. LM corrections ensure a balanced distribution of dissipation of kinetic energy in the limit of zero Mach number, thus extending the validity of compressible flow codes to Mach numbers as low as 10 -5 , and are particularly required for schemes providing accuracy less than 5 th -order [6]. The viscous terms are discretized by a second-order central scheme.…”

“…The solution is advanced in time by using a five-stage (fourth-order accurate) optimal strongstability-preserving Runge-Kutta method [7]. Further details of the numerical aspects of the code are given in [6] and [14] and references therein.…”

Experimental and Numerical Investigation of Forced Convection in a Double Skin Façade

“…Large eddy simulation (LES) has been used in many studies to analyze turbulent flows in simple geometries and boundary conditions [17][18][19][20]. Although this method gives more accuracy solution, it needs more computer memories than standard k-epsilon method.…”

Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations

“…The Mach number for the left and right states are calculated based on the velocity magnitude of all the velocity components independent of the normal direction in which the flux is computed. This modification is different in nature from a preconditioning step used for changing the flow variables, since our main motivation is not to relax the restriction in terms of the time-step size, but rather to increase the resolution at low speed regions, where this modification has demonstrated increased resolution and accuracy for a wide-range of flow problems [1,2,32,33,54], can be utilised with any Riemann solver and without computational overheads.…”

“…Considerable research efforts have been spent into the development, implementation and assessment of high-order finite volume (FV) discretisation schemes for DNS and LES [1,2]. High-order methods can achieve at least the same level of accuracy with second-order schemes but using coarser grids [3].…”