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291.
In this article, we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of steady solutions of the compressible fully coupled Reynolds‐averaged Navier–Stokes and k ? ω turbulence model equations for solving all‐speed flows. The system of equations is iterated to steady state by means of an implicit scheme. The DG solution is extended to the incompressible limit by implementing a low Mach number preconditioning technique. A full preconditioning approach is adopted, which modifies both the unsteady terms of the governing equations and the dissipative term of the numerical flux function by means of a new preconditioner, on the basis of a modified version of Turkel's preconditioning matrix. At sonic speed the preconditioner reduces to the identity matrix thus recovering the non‐preconditioned DG discretization. An artificial viscosity term is added to the DG discretized equations to stabilize the solution in the presence of shocks when piecewise approximations of order of accuracy higher than 1 are used. Moreover, several rescaling techniques are implemented in order to overcome ill‐conditioning problems that, in addition to the low Mach number stiffness, can limit the performance of the flow solver. These approaches, through a proper manipulation of the governing equations, reduce unbalances between residuals as a result of the dependence on the size of elements in the computational mesh and because of the inherent differences between turbulent and mean‐flow variables, influencing both the evolution of the Courant Friedrichs Lewy (CFL) number and the inexact solution of the linear systems. The performance of the method is demonstrated by solving three turbulent aerodynamic test cases: the flat plate, the L1T2 high‐lift configuration and the RAE2822 airfoil (Case 9). The computations are performed at different Mach numbers using various degrees of polynomial approximations to analyze the influence of the proposed numerical strategies on the accuracy, efficiency and robustness of a high‐order DG solver at different flow regimes. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
292.
In this paper, pressure‐based and density‐based methods are studied at different flow speeds. The methods are intended for steady flows, and the goal is to find as general an approach as possible to cover different Mach number regimes. The solution methods are based on a finite‐volume approach. Various forms of inviscid fluxes are applied and connected with either a pressure‐based or density‐based implicit solution. For this purpose, a new pressure‐correction method is developed that can be applied for incompressible and for compressible flows. Another option is a standard density‐based approximate factorization method. In both cases, a convergence is accelerated with a Full Approximation Scheme (FAS) multigrid approach. Sample problems in the range of Ma = 0…6 are simulated using different approaches, and their efficiency and accuracy are compared. On the basis of the quality of the solutions, recommendations are made. © 2015 The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd. 相似文献
293.
A time‐accurate algorithm is proposed for low‐Mach number, variable density flows on curvilinear grids. Spatial discretization is performed on collocated grid that offers computational simplicity in curvilinear coordinates. The flux interpolation technique is used to avoid the pressure odd–even decoupling of the collocated grid arrangement. To increase the stability of the method, a two‐step predictor–corrector time integration scheme is employed. At each step, the projection method is used to calculate the hydrodynamic pressure and to satisfy the continuity equation. The robustness and accuracy of the method is illustrated with a series of numerical experiments including thermally driven cavity, polar cavity, three‐dimensional cavity, and direct numerical simulation of non‐isothermal turbulent channel flow. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
294.
In the present work, we propose a reformulation of the fluxes and interpolation calculations in the PISO method, a well‐known pressure‐correction solver. This new reformulation introduces the AUSM+ ? up flux definition as a replacement for the standard Rhie and Chow method of obtaining fluxes and central interpolation of pressure at the control volume faces. This algorithm tries to compatibilize the good efficiency of a pressure based method for low Mach number applications with the advantages of AUSM+ ? up at high Mach number flows. The algorithm is carefully validated using exact solutions. Results for subsonic, transonic and supersonic axisymmetric flows in a nozzle are presented and compared with exact analytical solutions. Further, we also present and discuss subsonic, transonic and supersonic results for the well known bump test‐case. The code is also benchmarked against a very tough test‐case for the supersonic and hypersonic flow over a cylinder. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
295.
We develop in this paper a discretization for the convection term in variable density unstationary Navier–Stokes equations, which applies to low‐order non‐conforming finite element approximations (the so‐called Crouzeix–Raviart or Rannacher–Turek elements). This discretization is built by a finite volume technique based on a dual mesh. It is shown to enjoy an L2 stability property, which may be seen as a discrete counterpart of the kinetic energy conservation identity. In addition, numerical experiments confirm the robustness and the accuracy of this approximation; in particular, in L2 norm, second‐order space convergence for the velocity and first‐order space convergence for the pressure are observed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
296.
研究了甲烷-空气混合物爆轰波在二维突扩通道中传播的各种复杂行为。结果表明：爆轰波在进入突扩通道的初始阶段有局部向爆燃转变的现象;爆炸波在壁面发生马赫反射形成的高温高压区域将直接驱动自持爆轰波的重新形成。 相似文献
297.
A study of Mach shocks generated by fast partonic jets propagatingthrough the quark-gluon plasma (QGP) is reviewed briefly. We predict asignificant deformation of Mach shocks in central Au+Au collisions atRHIC and LHC energies compared to those created by a jet propagationthrough a static medium. Moreover, a new hydrodynamical study of jetenergy loss is presented. 相似文献
298.
The artificial compressibility method is extended to the case of unsteady turbulent reacting flows at low Mach number. The resulting scheme is applied to the calculation of a propagating one‐dimensional (1D) planar turbulent flame with a realistic heat release parameter. An eddy break‐up‐like approach, with a conventional gradient expression for the turbulent fluxes, is retained to model this reacting turbulent flow. A quenched form of the mean reaction rate is used to ensure the existence of a steady regime of propagation, for which the present results are compared with those obtained by a steady analysis of the mean flame brush structure, with excellent agreement. A sensitivity analysis of the convergence rate to the values of the artificial compressibility factor and the pseudo‐time is carried out. It is shown that a reduced artificial compressibility factor of 5–10, combined with a pseudo‐Courant number of ≈1000, represents a good compromise to optimize the convergence rate. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
299.
In the present study improvements to numerical algorithms for the solution of the compressible Euler equations at low Mach numbers are investigated. To solve flow problems for a wide range of Mach numbers, from the incompressible limit to supersonic speeds, preconditioning techniques are frequently employed. On the other hand, one can achieve the same aim by using a suitably modified acoustic damping method. The solution algorithm presently under consideration is based on Roe's approximate Riemann solver [Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43 : 357–372] for non‐structured meshes. The numerical flux functions are modified by using Turkel's preconditioning technique proposed by Viozat [Implicit upwind schemes for low Mach number compressible flows. INRIA, Rapport de Recherche No. 3084, January 1997] for compressible Euler equations and by using a modified acoustic damping of the stabilization term proposed in the present study. These methods allow the compressible Euler equations at low‐Mach number flows to be solved, and they are consistent in time. The efficiency and accuracy of the proposed modifications have been assessed by comparison with experimental data and other numerical results in the literature. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
300.
Shock reflection phenomena over nonstraight surfaces have been investigated. The models used in this experiment are ordinary
circular cylindrical concave and convex wedges and step-like wedges which simulate the former. The step-like wedges were used
to investigate the process of reflected-wave formation over circular cylindrical wedges (method of multiple steps). The reflected-wave
structure has been photographed with a schlieren apparatus. The formation of the reflected wave over circular cylindrical
wedges is physically well understood by comparing it with shock reflection over step-like wedges. In particular, the reason
why the reflected wave over a concave circular cylindrical wedge is very weak away from the reflection point is elucidated.
Moreover, the structure and the formation mechanism of the so-called transitioned regular reflection (TRR) are illustrated
in detail. As a by-product, based on acoustic theory, analytical formulae for the transition wedge angle are found. They are
in good agreement with experiments.
Received Received 28 February 1996 / Accepted 7 August 1996 相似文献