Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

Abstract

SUMMARYThe purpose of the present paper is to evaluate very-high-order upwind schemes for the direct numerical simulation (DNS) of compressible wall-turbulence. We study upwind-biased (UW) and weighted essentially nonoscillatory (WENO) schemes of increasingly higher order-of-accuracy (J.

Wall effects on pressure fluctuations in turbulent channel flow

“…Computed p rms corresponds, for the present dns results (Fig. 8), to the fluctuation of the actual thermodynamic pressure, obtained from the equation-of-state (Gerolymos et al 2010). There is quite good agreement of present results for p rms with the incompressible dns of Kim et al (1987), obtained with similar resolution on the same computational box (Fig.…”

“…For this reason the turbulent correlations obtained can be considered as incompressible. This has been verified by systematic comparison with standard incompressible pseudospectral dns data (Kim et al 1987;Moser et al 1999;delÁlamo & Jiménez 2003;delÁlamo et al 2004;Hoyas & Jiménez 2006, 2008, both for single point statistics (Gerolymos et al 2010, all soms † and toms ‡ appearing in the Reynolds-stress budgets) and for spectra of velocity fluctuations in the homogeneous [Lx, Ly, Lz (Nx, Ny, Nz) are the dimensions (number of grid-points) of the computational domain (x = homogeneous streamwise, y = normal-to-the-wall, z = homogeneous spanwise direction); δ is the channel halfheight; ∆x + , ∆y + w , ∆y + cl , ∆z + are the mesh-sizes in wall-units; (·)w denotes wall and (·)cl centerline values; N y + ≤10 is the number of grid points between the wall and y + = 10; Reτ w :=ūτ δν −1 w ;ūτ is the friction velocity; δ is the channel halfheight;νw = is the kinematic viscosity at the wall;Mcl is the centerline Mach-number; ∆t + is the computational time-step in wall-units; t + obs is the observation period in wall units over which statistics were computed; ∆t + s is the sampling time-step for the single-point statistics in wall-units; ∆t + s R 2 is the sampling time-step for the two-point statistics in wall-units].…”

“…The methodology described in the present paper is independent of the particular dns solver used. The dns database was generated for Re τw :=ū τ δν −1 = 180 (where 2δ = L y is the channel height, u τ := τ w ρ −1 is the friction velocity and ν the kinematic viscosity) using the dns solver described and validated in Gerolymos et al (2010), which solves the flow-equations in physical et al (1999) […”

“…7) with the instantaneous p -field directly computed (without making use of Green's functions) by the compressible dns solver (Gerolymos et al 2010 (Fig. 8) with standard results from incompressible dns computations (Kim et al 1987;Hoyas & Jiménez 2008), both in the wall and the outer regions (Fig.…”

“…Distributions of the 5 terms in the incompressible p -splitting (2.10) of pressure transport, p (r;V) u i , p (r;w) u i , p (s;V) u i , p (s;w) u i , and p (τ ) u i , from the present dns computations (Reτ w = 179;Mcl = 0.34; 193 × 129 × 169 grid; Tab. 1), distributions of pressure transport p u i from various dns databases (Moser et al 1999;Hoyas & Jiménez 2008;Gerolymos et al 2010), and corresponding contributions to the pressure-diffusion tensor d (p) ij , in wall units, plotted against the nondimensional distance from the wall y + (in fully developed incompressible plane channel flow…”