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Summary: Weighted compact nonlinear schemes (WCNSs) are a popular family of high‐resolution shock‐capturing schemes for simulating compressible flows, of which the nonlinear interpolation procedure is dominant for the performance. In this work, a simplified weighting strategy is introduced for the nonlinear interpolation procedure. Firstly, an equivalent weighting formulation of WCNS is presented by explicitly including the whole‐point stencil into the set of candidate stencils. Secondly, motivated by the reorganization of WCNS, the WCNS‐CU6 scheme is achieved in a more straightforward way. Thirdly, by introducing a TENO selection procedure in the framework of WCNS‐CU6‐Simplified, a TCNS6‐Simplified scheme is proposed, the resolution of which is comparable with the excellent TENO6 scheme, while the computational cost is much lower. The simplified schemes exhibit more outstanding, at least comparable, fidelity than the original schemes, however, with superior characteristics in terms of efficiency and simplicity. A variety of benchmark test problems are studied to demonstrate the behaviour of the simplified weighting strategy. [ABSTRACT FROM AUTHOR]

There are still some challenges, such as grid quality, numerical stability, and boundary schemes, in the practical application of high-order finite difference schemes for complex configurations. This study presents some improved strategies that indicate potential engineering applications of high-order schemes. The formally fifth-order weighted compact nonlinear scheme developed by the authors is implemented on point-matched multiblock structured grids, which are generated over complex configurations to ensure the grid quality of each component block. The information transmission between neighboring blocks is carried out by new characteristic-based interface conditions that directly exchange the spatial derivatives on each side of an interface by means of a characteristic-based projection to keep the high-order accuracy and high resolution of a spatial difference scheme. The high-order scheme combined with the interface conditions is shown to be asymptotically stable. The engineering-oriented applications of the high-order strategy are demonstrated by solving several two- and three-dimensional problems with complex grid systems. DOI: 10.2514/1.J050285

Near-space hypersonic flow usually has concomitant circumstances with multiple complex physical, chemical and fluid mechanic such as real gas effects, rarefied effects, and viscous interactions. Regarding the topic of multi-physics phenomena in the hypersonic flow past complex lift-body configurations, the studies on the hypersonic aerodynamic characteristics of American shuttle orbiter were briefly reviewed for the phase of pre-flight and post-flight, respectively. For the pre-flight phase, the studies were introduced with respect to extrapolating parameter of the aerodynamic data and the uncertainty quantity. Hypersonic viscous parameter was employed as the extrapolating factor of the aerodynamic characteristics, and the computational method was introduced for the uncertainty quantity of the aerodynamic forces. The introduction of the post-flight phase included the comparison between the predicted data and the flight tests, the longitudinal trim anomaly analysis, and the extrapolating method for the flight data. The preliminary method, extrapolating the wind-tunnel data to the flight data, was surveyed. The influence of the real gas effects was identified on the aerodynamic characteristics; however, it is still uncertain that the real gas effects have influence on the control surfaces efficiency. Finally, four issues, i. e., the probability of avoiding longitudinal trim anomaly, the differences of the body-flap efficiency between the calculations and the experiments, the studies of the aerodynamics uncertainty with various approaches, and the establishment of a sharing system for data from the flight tests, the tunnel tests and the CFD are discussed. In addition, it is mentioned in the early studies that the multi-physics phenomena co-exist during the space shuttle reentry, and it is difficult to discern the individual effect on the aerodynamic characteristics under the research conditions at that time. In the late studies, it has not been focused on that the coupled effects of these phenomena on the aerodynamics characteristics of the space shuttle. This lack of investigations provides a further research field for the studies of multi-physics phenomena. [ABSTRACT FROM AUTHOR]

The quasi-linear spectral analysis method based on an approximate dispersion relation (ADR) can give spectral properties of nonlinear space-discrete schemes more accurately. It has become to be a very important tool for the assessment of nonlinear schemes up to date. However, some factors, such as time-discrete schemes and number of computation grid points, may affect the prediction accuracy seriously and make the ADR formula hard to be employed. In some cases, the spectral curve may even jump at some points under some conditions. In order to develop the formula independent of the influences of these factors, time-discrete independent ADR formula is proposed firstly through theoretical analysis. The meanings of each term in the ADR formula are explained, and the influence of time step on the time dependent ADR is investigated. Secondly, the reason resulting in the curve jumps at some wave numbers is analyzed using this new time-independent ADR formula. It is shown that the jumps may happen in case the number of grid points is improperly chosen. The proper method to selected grid points number is introduced, the proposed formula may eliminate the influence of number of grid points and initial phase angle effectively when the number of grid points is larger than this supposed number. Based on these works, the spectral properties of two 3rd-order WCNS schemes are investigated, and some typical cases are simulated using these two schemes. The results show that the quasi- linear spectral curve calculated by the ADR formula evaluates the properties of nonlinear schemes qualitatively. However, in respect of quantity, the errors cannot be ignored. [ABSTRACT FROM AUTHOR]

Noise prediction using high-order numerical method is one of the most interested research topics in CFD. HDCS-E8T7 scheme is a seventh-order hybrid linear compact dissipative scheme. This scheme overcomes the disadvantage that many high-order finite difference schemes may have when geometric conservation law (GCL) is not satisfied, the numerical instability phenomenon may be avoided when the HDCS-E8T7 is applied to solve aeroacoustic problem in complex geometry. In the present high-order numerical noise prediction method, the spatial discretization adopts HDCS-E8T7 scheme and its boundary schemes have suitable accuracy comparing with the interior scheme. High-order multi-step Runge-Kutta and dual stepping scheme are employed for time integration, high-order interface boundary scheme is developed to extend the present method to multi-block point matched grid which meets the need of solving problem in complex geometry and the turbulence is handled by the concept of implicit large eddy simulation. Based on this method, the effect of GCL on the numerical solutions is studied. The importance of satisfying the GCL on complex grid for high-order simulation is illuminated. Some typical noise cases, such as vortex convection, scattering of acoustic waves by multiple cylinder, sound radiated by a rod-airfoil configuration and jet noise from nozzle, are investigated. The solutions of these tests show that the presented method has high prediction accuracy and potential application for handling aeroacoustic problem on complex geometry. [ABSTRACT FROM AUTHOR]

Based on CARDC hypersonic numerical simulation platform Chant-2. 0, applications of γ-Reθ model to hypersonic boundary layer transition are investigated preliminarily. The transition onset and length are predicted by solving two transport equations for turbulence intermittency factor and momentum thickness Reynolds number. Firstly, γ-Reθ transition model using local correlation functions is calibrated through four cases of low speed flat flows, and in the process freestream turbulence intensities have a wide range from low level natural transition to high level bypass transition. Then, taking account of flow properties of hypersonic boundary layer, the pressure gradient function used in the transition model's Reθ correlation is properly modified for high Mach number flows. Finally, by adopting the new model functions, hypersonic boundary layer transitions of flat and sharp cone are calculated and compared with referrence data. The simulation results indicate that the specially calibrated correlations for hypersonic platform software can accurately predict the onset and length of transition region in low speed cases, and high Mach number correction shows good performance in hypersonic simulations. [ABSTRACT FROM AUTHOR]