一种简单的精确捕捉接触间断的黎曼求解器

基于Godunov型数值格式的有限体积法是求解双曲型守恒律系统的主流方法,其中用来计算界面数值通量的黎曼求解器在很大程度上决定了数值格式在计算中的表现。单波的Rusanov求解器和双波的HLL求解器具有简单、高效和鲁棒性好等优点,但是在捕捉接触间断时耗散太大。全波的HLLC格式能够精确捕捉接触间断,但是在计算中出现的激波不稳定现象限制了其在高马赫数流动问题中的应用。本文利用双曲正切函数和五阶WENO格式来重构界面两侧的密度值,并且结合边界变差下降算法来减小Rusanov格式耗散项中的密度差,从而提高格式对于接触间断的分辨率。研究表明,相比于全波的HLLC求解器,本文构造的黎曼求解器不仅具有更高的接触分辨率,而且还具有更好的激波稳定性。     

A new high-accuracy scheme for compressible turbulent flows

Shock-capturing and broad-bandwidth scale resolutions are two main challenges of compressible turbulent flow simulation. To meet the rigorous requests, a novel fifth-order hybrid scheme based on a uniform hybrid framework is designed. With the help of a continuous weight operator, the new scheme combines an upwind compact scheme for smooth regions and a compact-reconstruction weighted essentially non-oscillatory scheme for discontinuous regions. Numerical analyses and canonical numerical tests confirm that the new scheme has high accuracy, spectral-like resolution property and shock-capturing capability. Besides, the new scheme shows high computational efficiency compared to the related shock-capturing schemes and hybrid ones.     

A generalized Rusanov method for the Baer‐Nunziato equations with application to DDT processes in condensed porous explosives

The paper addresses a numerical approach for solving the Baer‐Nunziato equations describing compressible 2‐phase flows. We are developing a finite‐volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer‐Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration‐to‐detonation transition (DDT) in porous reactive materials.     

Calculation of supersonic flow around v-shaped wings by the fitting method

The problem of flow around a V-shaped wing with supersonic leading edges is solved. The method employed is that of fitting with respect to a space variable in which the system of equations of motion is hyperbolic, using the computing scheme of V. V. Rusanov, A comparison between the results of these calculations and experimental data in relation to the pressure distribution along the wing span reveals excellent agreement, except for a limited region, in which the compression jump incident on the plane of the wing interacts with the boundary layer. A comparison between the results obtained by means of the oblique-jump equations and by numerical calculations indicates that the method in question is reasonably accurate.Translated from Izvestiya Akademu Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–185, May–June, 1971.The author is grateful to A. L. Gonor and V. V. Rusanov for interest in this work.     

Calculations of 3D compressible flows using an efficient low diffusion upwind scheme

A newly suggested E‐CUSP upwind scheme is employed for the first time to calculate 3D flows of propulsion systems. The E‐CUSP scheme contains the total energy in the convective vector and is fully consistent with the characteristic directions. The scheme is proved to have low diffusion and high CPU efficiency. The computed cases in this paper include a transonic nozzle with circular‐to‐rectangular cross‐section, a transonic duct with shock wave/turbulent boundary layer interaction, and a subsonic 3D compressor cascade. The computed results agree well with the experiments. The new scheme is proved to be accurate, efficient and robust for the 3D calculations of the flows in this paper. Copyright © 2005 John Wiley & Sons, Ltd.     

Implicit large eddy simulation of a supersonic flat-plate boundary layer flow by weighted compact nonlinear scheme

The performance of implicit large eddy simulation (ILES) of a supersonic flat-plate turbulent boundary layer flow by weighted compact nonlinear scheme (WCNS) has been investigated. In view of features of WCNS and ILES, it was expected that ILES by WCNS could be an efficient approach to perform LES of supersonic turbulent flows. The flowfield calculated by WCNS was of lower turbulent intensity compared with an explicit LES data obtained by a numerical scheme of the same order of accuracy on a computational grid of similar resolution. It was concluded that the numerical dissipation inherent in WCNS is so large that applying WCNS to ILES of this flowfield is inefficient compared with explicit LES.     

一种健壮的混合Roe黎曼求解器

使用Roe格式计算多维流动问题时,在强激波附近会出现数值激波不稳定现象。带有剪切粘性的HLLEC格式不仅可以捕捉接触间断,而且表现出很好的稳定性。混合Roe格式和HLLEC格式来消除数值激波不稳定性。在强激波附近,通过激波面法向和网格界面法向的夹角来定义开关函数,使得数值通量在激波面横向切换成HLLEC格式。在其余地方,数值通量依然使用Roe格式来计算。数值试验表明,混合格式不仅消除了Roe格式的数值激波不稳定性,还最大程度地减少了HLLEC格式所带来的剪切耗散,保留了Roe格式高分辨率的优点。     

High‐order shock capturing schemes for turbulence calculations

This work investigates high‐order central compact methods for simulating turbulent supersonic flows that include shock waves. Several different types of previously proposed characteristic filters, including total variation diminishing, monotone upstream‐centered scheme for conservation laws, and weighted essentially non‐oscillatory filters, are investigated in this study. Similar to the traditional shock capturing schemes, these filters can eliminate the numerical instability caused by large gradients in flow fields, but they also improve efficiency compared with classical shock‐capturing schemes. Adding the nonlinear dissipation part of a classical shock‐capturing scheme to a central scheme makes the method suitable for incorporation into any existing central‐based high‐order subsonic code. The amount of numerical dissipation to add is sensed by means of the artificial compression method switch. In order to improve the performance of the characteristic filters, we propose a hybrid approach to minimize the dissipation added by the characteristic filter. Through several numerical experiments (including a shock/density wave interaction, a shock/vortex interaction, and a shock/mixing layer interaction) we show that our hybrid approach works better than the original method, and can be used for future turbulent flow simulations that include shocks. Copyright © 2009 John Wiley & Sons, Ltd.     

Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods

In this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5% extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high‐order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high‐order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock‐capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high‐order weighted compact nonlinear scheme is not only robust for shock‐capturing but also accurate for hypersonic heat transfer prediction. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulation of compressible turbulent flow via improved gas‐kinetic BGK scheme

In order to solve compressible turbulent flow problems, this study focuses on incorporating the Spalart–Allmaras turbulence model into gas‐kinetic BGK (Bhatnagar–Gross–Krook) scheme. The Spalart–Allmaras turbulence model is solved using finite difference discretization. The variables on the cell interface are interpolated via the van Leer limiter in the reconstruction stage. Simulation of subsonic and transonic flow over a NACA0012 airfoil has been implemented using two‐dimensional body‐fitted grids. The numerical results obtained appear in good agreement with the AGARD results, demonstrating the effectiveness and usefulness of the strategy of coupling the Spalart–Allmaras turbulence model with the BGK scheme for compressible turbulent flow simulation. Copyright © 2010 John Wiley & Sons, Ltd.