Direct numerical simulation of passive scalar in decaying compressible turbulence

1IntroductionDirectnumericalsimulation(DNS)becomesanimportanttoolinrecentresearchofturbulence[1].DNSofcompressibleturbulenceismoredifficultthanthatoftheincompressibleturbulence.WhentheturbulentMachnumberisgreaterthan0.3theshockletsmayappearinthecompressibleturbulentflowfields.Thereasonandmechanismofshockletsexistencearenotclearyet.TheturbulentMachnumberinDNScannotbeveryhighwiththepresentexistingnumericalmethodsandcomputerresource.Fortheproblemofcompressibleisotropicturbulencewiththeinitia…     

On the efficient application of weighted essentially nonoscillatory scheme

In this paper, the efficient application of high‐order weighted essentially nonoscillatory (WENO) reconstruction to the subsonic and transonic engineering problems is studied. On the basis of the physical considerations, two techniques are proposed to enhance the accuracy and efficiency of the WENO reconstruction. First, it is observed that the WENO scheme using characteristic variable has better accuracy and convergence speed than the scheme using primitive variable. For engineering problems with shock of moderate amplitude, on the basis of the Rankine–Hugoniot conditions, a simplified characteristic‐variable‐based WENO is developed. The simplified version significantly reduces the cost overhead without sacrificing the shock‐capturing capability. Second, in this work, it is found for viscous case that it is better to include the viscous effect. On the basis of a simple analysis, the viscous correction to the parameter ε in the WENO reconstruction is proposed. Numerical results indicate, with the proposed simplified characteristic‐variable‐based reconstruction and the viscous correction, that the nonlinear WENO interpolation is sharply activated in the region of shock jump, whereas in the shockless area, the WENO interpolation weights are tuned towards the designed optimal value for better accuracy. Compared with the original characteristic‐variable‐based WENO, the current implementation has similar accuracy and reduced cost. At the same time, compared with the primitive variable‐based WENO, better accuracy and convergence speed are obtained at marginal cost overhead. Several practical cases are calculated to demonstrate the accuracy and efficiency of the current methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations

In this paper, we consider the Cauchy problem for the three dimensional chemotaxis-Navier–Stokes equations. By exploring the new a priori estimates, we prove the global existence of weak solutions for the 3D chemotaxis-Navier–Stokes equations.     

A stochastic lagrangean picture for the three dimensional navier-stokes equation +

We derive a representation formula for the solutions of the navier-Stokes flow in three dimensions in absence of boundary in terms of stochastic current lines. This pictures generalizes an analogous one given in two dimensions and on the other hand the classical Lafrangian picture for the Euler flow. We prove a Vanishing viscosity limit for the whole structure     

SPH simulation of oblique shocks in compressible flows

The Lagrangian smoothed particle hydrodynamics (SPH) method is used to simulate shock waves in inviscid, supersonic (compressible) flow. It is shown for the first time that the fully Lagrangian SPH particle method, without auxiliary grid, can be used to simulate shock waves in compressible flow. The wall boundary condition is treated with ghost particles combined with a suitable repulsive potential function, whilst corners are treated by a novel ‘angle sweep’ technique. The method gives accurate predictions of the flow field and of the shock angle as compared with the analytical solution. The study shows that SPH is a good potential candidate to solve complex aerodynamic problems, including those involving rarefied flows, such as atmospheric re‐entry. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical investigation of the effects of sluice spillway roof profiles on the hydraulic characteristics

There is a need for evolving hydraulically efficient roof profile of bellmouth for high head sluice spillways, as sluice roof is susceptible to cavitation damage. In this paper, formulation and development of a numerical model for simulating the spillway flow and its application to a sluice spillway are presented. The main focus of the simulation study is to apply the developed model to investigate the effects of sluice roof profile geometry on the pressure distribution, the discharge coefficient and the nature of flow regime within the sluice bellmouth. From the analysis of results for eight different roof profiles by varying the entry and exit angles of elliptic bellmouth transition, some important observations have been suggested, which are of practical relevance to hydraulic design engineers. The numerical model results are compared for one profile with physical model study. The simulated results are in close agreement with the measured values. Copyright © 2007 John Wiley & Sons, Ltd.     

Conceptual linearization of Euler governing equations to solve high speed compressible flow using a pressure‐based method

The main objective of the current work is to introduce a new conceptual linearization strategy to improve the performance of a primitive shock‐capturing pressure‐based finite‐volume method. To avoid a spurious oscillatory solution in the chosen collocated grids, both the primitive and extended methods utilize two convecting and convected momentum expressions at each cell face. The expressions are obtained via a physical‐based discretization of two inclusive statements, which are constructed via a novel incorporation of the continuity and momentum governing equations. These two expressions in turn provide a strong coupling among the Euler conservative statements. Contrary to the primitive work, the linearization in the current work respects the definitions and essence of physics behind deriving the Euler governing equations. The accuracy and efficiency of the new formulation are then investigated by solving the shock tube as a problem with moving normal and expansion waves and the converging‐diverging nozzle as a problem with strong stationary normal shock. The results show that there is good improvement in performance of the primitive pressure‐based shock‐capturing method while its superior accuracy is not deteriorated at all. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

The present paper investigates the multigrid (MG) acceleration of compressible Reynolds‐averaged Navier–Stokes computations using Reynolds‐stress model 7‐equation turbulence closures, as well as lower‐level 2‐equation models. The basic single‐grid SG algorithm combines upwind‐biased discretization with a subiterative local‐dual‐time‐stepping time‐integration procedure. MG acceleration, using characteristic MG restriction and prolongation operators, is applied on meanflow variables only (MF–MG), turbulence variables being simply injected onto coarser grids. A previously developed non‐time‐consistent (for steady flows) full‐approximation‐multigrid (s–MG) is assessed for 3‐D anisotropy‐driven and/or separated flows, which are dominated by the convergence of turbulence variables. Even for these difficult test cases CPU‐speed‐ups r_CPUSUP∈[3, 5] are obtained. Alternative, potentially time‐consistent approaches (unsteady u–MG), where MG acceleration is applied at each subiteration, are also examined, using different subiterative strategies, MG cycles, and turbulence models. For 2‐D shock wave/turbulent boundary layer interaction, the fastest s–MG approach, with a V(2, 0) sawtooth cycle, systematically yields CPU‐speed‐ups of 5±½, quasi‐independent of the particular turbulence closure used. Copyright © 2008 John Wiley & Sons, Ltd.     

SUPERCONVERGENCE OF THE FULL-DISCRETE F.E.M. FOR COMPRESSIBLE MISCIBLE DISPLACEMENT: THE FULL TENSOR CASE

1　ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｓｈａｌｌｃｏｎｓｉｄｅｒｔｈｅｍｏｄｅｌｆｏｒｍｉｓｃｉｂｌｅｄｉｓｐｌａｃｅｍｅｎｔｏｆｏｎｅｃｏｍｐｒｅｓｓｉｂｌｅｆｌｕｉｄｂｙａｎｏｔｈｅｒｉｎａｈｏｒｉｚｏｎｔａｌｒｅｓｅｒｖｏｉｒΩ Ｒ2 ｏｆｕｎｉｔｔｈｉｃｋｎｅｓｓｄｅｓｃｒｉｂｅｄｂｙｔｈｅｎｏｎｌｉｎｅａｒｐａｒａｂｏｌｉｃｓｙｓｔｅｍ[6]ｄ(ｃ) ｐ ｔ+ ·ｕ =ｄ(ｃ) ｐ ｔ- · (ａ(ｃ) ｐ) =ｑ ,(1.1)φ ｃ ｔ+ｂ(ｃ) ｐ ｔ+ｕ· ｃ - · (Ｄ(ｕ) ｃ =(^ｃ -ｃ)ｑ ,(1.2 )ｕ·ν =(Ｄ(ｕ) ｃ-ｃｕ)…     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.