Dynamic optimization methodology based on subgrid-scale dissipation for large eddy simulation

A dynamic procedure based on subgrid-scale dissipation is proposed for large eddy simulation of turbulent flows. In the new method, the model coefficients are determined by minimizing the square error of the resolved dissipation rate based on the Germano identity. A dynamic two-term mixed model is tested and evaluated both a priori and a posteriori in simulations of homogeneous and isotropic turbulence. The new dynamic procedure proves to be more effective to optimize the model coefficients as compared with traditional method. The corresponding dynamic mixed model can predict the physical quantities more accurately than traditional dynamic mixed model. (C) 2016 AIP Publishing LLC

Optimized sixth-order monotonicity-preserving scheme by nonlinear spectral analysis

In this paper, sixth-order monotonicity-preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed on the basis of the dispersion and dissipation optimization and monotonicity-preserving technique. The nonlinear spectral analysis method is developed and is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. The new scheme (OMP6) is simple in expression and is easy for use in CFD codes. The suitability and accuracy of this new scheme have been tested through a set of one-dimensional, two-dimensional, and three-dimensional tests, including the one-dimensional Shu-Osher problem, the two-dimensional double Mach reflection, and the Rayleigh-Taylor instability problem, and the three-dimensional direct numerical simulation of decaying compressible isotropic turbulence. All numerical tests show that the new scheme has robust shock capturing capability and high resolution for the small-scale waves due to fewer numerical dispersion and dissipation errors. Moreover, the new scheme has higher computational efficiency than the well-used WENO schemes

Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects

Direct numerical simulations (DNS) were performed to investigate the interactions of a Mach 2.9 turbulent boundary layer with shock waves of varying strengths in compression corner. The supersonic turbulent boundary layer was triggered by wall blowing-and-suction perturbations. The shock waves were produced by two-dimensional compression corners of 8, 14, 20 and 24 degrees. Compared with previous DNS results and experimental data, the numerical calculations were validated. The effects of shock wave on the boundary layer are studied by both flow visualizations and statistical analysis, and the results show that the intensity of fluctuations is amplified greatly by the shock wave. With the increasing of turning angle, three-dimensionality of separation bubble is significantly enhanced. Based on the statistics and power spectrum of the wall pressure signals, the effect of turning angle on the unsteadiness of shock motion is also studied, and the results show that the shock motions are quite different in the small and the large turning angle cases. The motion in the 8 and 14 cases is characterized by high-frequency and small amplitude, but the low-frequency and large-scale streamwise oscillation is the main feature in the 20 and 24 cases. The effect of turning angle on the turbulence state is analyzed by using the anisotropy of Reynolds stress tensor. The coherent vortex structures are also studied qualitatively. The results indicate that the cane-like streamwise vortexes in the near-wall region are the dominant structure for the small angle cases, while the hairpin vortexes and packets in the outer layer play the leading role in the large angle cases. According to the quantitative analysis of turbulent kinetic energy budgets in the separation region, the effect of turning angle on the transport mechanism is studied. It is found that the influence of shear layer above separation bubble on the mechanism is significant. (C) 2017 Elsevier Ltd. All rights reserved

COMMUNICATIONS IN COMPUTATIONAL PHYSICS

In this paper, direct numerical simulation (DNS) is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma(infinity) = 2.25,5,6,8. When Ma(infinity) = 8, two cases with the ratio of wall-to-reference temperature T-w/T-infinity = 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-infinity = 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

Bell-Plessett effect on harmonic evolution of spherical Rayleigh-Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers

Based on the harmonic analysis [Liu et al. Phys. Plasmas 22 112112 (2015)] the analytical investigation on the harmonic evolution in Rayleigh-Taylor instability (RTI) at a spherical interface has been extended to the general case of arbitrary Atwood numbers by using the method of the formal perturbation up to the third order in a small parameter. Our results show that the radius of the initial interface [i.e. Bell-Plessett (BP) effect] dramatically influences the harmonic evolution for arbitrary Atwood numbers. When the initial radius approaches infinity compared against the initial perturbation wavelength the amplitudes of the first four harmonics will recover those in planar RTI. The BP effect makes the amplitudes of the zeroth second and third harmonics increase faster for a larger Atwood number than smaller one. The BP effect reduces the third-order negative feedback to the fundamental mode for a smaller Atwood number and strengthens it for a larger one. Hence the BP effect helps the fundamental mode grow faster for a smaller Atwood number. Published by AIP Publishing

An Adaptive Multimoment Global Model on a Cubed Sphere

An adaptive global shallow-water model is proposed on cubed-sphere grid using the multimoment finite volume scheme and the Berger-Oliger adaptive mesh refinement (AMR) algorithm that was originally designed for a Cartesian grid. On each patch of the cubed-sphere grid, the curvilinear coordinates are constructed in a way that the Berger-Oliger algorithm can be applied directly. Moreover, an algorithm to transfer data across neighboring patches is proposed to establish a practical integrated framework for global AMR computation on the cubed-sphere grid. The multimoment finite volume scheme is adopted as the fluid solver and is essentially beneficial to the implementation of AMR on the cubed-sphere grid. The multimoment interpolation based on both volume-integrated average (VIA) and point value (PV) provides the compact reconstruction that makes the present scheme very attractive not only in dealing with the artificial boundaries between different patches but also in the coarse fine interpolations required in the AMR computations. The single-cell-based reconstruction avoids involving more than two nesting levels during interpolations. The reconstruction profile of constrained interpolation profile-conservative semi-Lagrangian scheme with third-order polynomial function (CIP-CSL3) is adopted where the slope parameter provides a flexible and convenient switching to get the desired numerical properties, such as high-order (fourth order) accuracy, monotonicity, and positive definiteness. Numerical experiments with typical benchmark tests for both advection equation and shallow-water equations are carried out to evaluate the proposed model. The numerical errors and the corresponding CPU times of numerical experiments on uniform and adaptive meshes verify the performance of the proposed model. Compared to the uniformly refined grid, the AMR technique is able to achieve the similar numerical accuracy with less computational cost

Direct Numerical Simulation of Compressible Turbulent Flows

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