A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expression and is easy for use in CFD codes.Compared with the original second-order or third-order MUSCL scheme,the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves.This new scheme has been tested through a set of one-dimensional and two-dimensional tests,including the Shu-Osher problem,the Sod problem,the Lax problem,the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test.All numerical tests show that,compared with the original MUSCL schemes,the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.
In this paper,direct numerical simulation(DNS)is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma∞=2.25,5,6,8.When Ma∞=8,two cases with the ratio of wall-to-reference temperature T_(w)/T_(∞)=1.9 and 10.03 are considered respectively.The wall temperature approaches recovery temperatures for other cases.The characteristics of compressible turbulent boundary layer(CTBL)affected by freestream Mach number and wall temperature are investigated.It focuses on assessing compressibility effects and the validity of Morkovin’s hypothesis through computing and analyzing the mean velocity profile,turbulent intensity,the strong Reynolds analogy(SRA)and possibility density function of dilatation term.The results show that,when the wall temperature approaches recovery temperature,the effects of Mach number on compressibility is insignificant.As a result,the compressibility effect is very weak and the Morkovin’s hypothesis is still valid for Mach number even up to 8.However,when Mach number equal to 8,the wall temperature effect on the compressibility is sensitive.In this case,when T_(w)/T_(∞)=1.9,the Morkovin’s hypothesis is not fully valid.The validity of classical SRA depends on wall temperature directly.A new modified SRA is proposed to eliminate such negative factor in near wall region.Finally the effects of Mach number and wall temperature on streaks are also studied.
In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.
This paper reviews the authors' recent studies on compressible turbulence by using direct numerical simulation (DNS),including DNS of isotropic(decaying) turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.
This paper reports the direct numerical simulation (DNS) for hypersonic turbulent boundary layer over a flat-plate at Ma∞ =8 with the ratio of wall-to-freestream temperature equal to 1.9, which indicates an extremely cold wall condition. It is primarily used to assess the wall temperature effects on the mean velocity profile, Walz equation, turbulent intensity, strong Reynolds analogy (SRA), and compressibility. The present high Mach number with cold wall condition induces strong compressibility effects. As a result, the Morkovin's hypothesis is not fully valid and so the classical SRA is also not fully consistent. However, some modified SRA is still valid at the far-wall region. It is also verified that the semi-local wall coordinate y* is better than conventional y+ in analysis of statistics features in turbulent boundary layer (TBL) in hypersonic flow.
