An adaptive implicit–explicit scheme for the DNS and LES of compressible flows on unstructured grids

An adaptive implicit–explicit scheme for Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) of compressible turbulent flows on unstructured grids is developed. The method uses a node-based finite-volume discretization with Summation-by-Parts (SBP) property, which, in conjunction with Simultaneous Approximation Terms (SAT) for imposing boundary conditions, leads to a linearly stable semi-discrete scheme. The solution is marched in time using an Implicit–Explicit Runge–Kutta (IMEX-RK) time-advancement scheme. A novel adaptive algorithm for splitting the system into implicit and explicit sets is developed. The method is validated using several canonical laminar and turbulent flows. Load balance for the new scheme is achieved by a dual-constraint, domain decomposition algorithm. The scalability and computational efficiency of the method is investigated, and memory savings compared with a fully implicit method is demonstrated. A notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed.     

An adaptive multiresolution scheme with local time stepping for evolutionary PDEs

We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge–Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction–diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability.     

Injection and mixing in a scramjet combustor: DES and RANS studies

The low momentum flux ratio jet in the HyShot II scramjet combustor is studied by DES (Detached Eddy Simulation) and RANS (Reynolds-Averaged Navier–Stokes) methods. The flow structure near the injector, shock pattern in the symmetry plane as well as the instantaneous coherent structures are presented and explained. Further insight into the flow physics is obtained by visualizing instantaneous coherent structures. The formation of Ω-shaped vortices, which was previously observed in experiments but never well-studied numerically, is discussed in detail. A new schematic of flow physics is proposed to enhance the understanding of the low momentum flux ratio jet. Compared to the DES result, the RANS method is unable to capture the dynamics of turbulent structures. The DES method provides much detailed information about mixing patterns and a more reliable mixing efficiency than the RANS result. The RANS method over-predicts the eddy-viscosity during turbulence modeling and suppresses unsteady turbulent fluctuations by time averaging, which results in a 25% over-estimation of the mixing efficiency.     

Numerical visualization of vortical structures in a spatially evolving turbulent compressible mixing layer

Large-eddy simulations are performed to numerically visualize the generation of streamwise vortical structures and its interaction with spanwisely rolled-up coherent vortical structure during the spatial development of a turbulent supersonic/subsonic mixing layer at convective Mach numberM _c =0.51. Time-dependent three-dimensional compressible conservation equations were solved with a subgrid-scale turbulence model. The numerical code used the finite-volume technique, which adopted alternately in temporal discretization the second-order, explicit MacCormack’s and modified Godunov’s schemes. Both transverse and spanwise perturbations were imposed initially for promoting the formation of spanwise rollers and counter-rotating streamwise vortices, respectively. Numerical visualizations are presented in terms of time-sequence isopressure surfaces and vorticity contours of spanwise and streamwise components. The results show that the spatial growth of three-dimensional vortical structures, in particular, the formation of chain-link-fence type structures, is adequately captured by the present computations. Vorticity dynamics is further analyzed, for the first time, to identify the dominant roles played by the convection effect followed by the vortex stretching effect on affecting the evolution of streamwise and spanwise vortical structures, respectively, forM _c <0.6.     

Statistical and coherence effects in nonlinear optical parametric up conversion. II. Incoherent interaction

Parametric up conversion (PUC) by incoherent nonlinear optical mixing of second-order coherent strong pumping radiation and another weak chaotic input radiation with a finite spectral width is treated in the second part of this paper. The efficiency of PUC is calculated in the second approximation of the iterative method. It is shown that in the case of perfect phase matching the efficiency of PUC decreases with increase of both the spectral width of the input radiation and the dispersion of medium, whilst at considerable values of phase mismatch the reverse effect appears. The spectral distribution of the resulting sum-frequency radiation is calculated in the first approximation of the iterative method. There is a general tendency to narrowing of the spectral distribution of the generated radiation in the course of PUC. Moreover, when there is a phase mismatch present, a spectral shift of the central maximum of generated radiation towards the blue or red region, according to the signs of the phase mismatch and the typical dispersion coefficient, appears in the later phases of the PUC.     

Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method

The aim of the present paper is to report on our recent results for GPU accelerated simulations of compressible flows. For numerical simulation the adaptive discontinuous Galerkin method with the multidimensional bicharacteristic based evolution Galerkin operator has been used. For time discretization we have applied the explicit third order Runge-Kutta method. Evaluation of the genuinely multidimensional evolution operator has been accelerated using the GPU implementation. We have obtained a speedup up to 30 (in comparison to a single CPU core) for the calculation of the evolution Galerkin operator on a typical discretization mesh consisting of 16384 mesh cells.     

Separation and suppression of coherent transfer effects in two-dimensional NOE and chemical exchange spectroscopy

A new method for the separation of coherent and incoherent magnetization transfer in two-dimensional (2D) NOE and chemical exchange spectroscopy is described. The new experiment differs from previous 2D exchange experiments, in that the mixing time τ_m is incremented systematically together with the evolution time t₁. This permits the distinction of the different orders of multiple-quantum coherence during the mixing time and allows the separation of coherent and incoherent transfer processes. The resulting clarification of chemical exchange and 2D NOE spectra is illustrated with experiments on small molecules and on a globular protein, the basic pancreatic trypsin inhibitor.     

Coherent structure extraction in turbulent channel flow using boundary adapted wavelets

We introduce boundary adapted wavelets, which are orthogonal and have the same scale in the three spatial directions. The construction thus yields a multiresolution analysis. We analyse direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows us to split the flow into two parts, coherent and incoherent flows. The coherent vorticity is reconstructed from its few intense wavelet coefficients and the coherent velocity is reconstructed using Biot–Savart's law. The statistics of the coherent flow, i.e. energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets of the total flow are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e. noise-like, background flow whose energy is equidistributed.     

A second-order discretization of the nonlinear Poisson–Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids

In this paper we present a finite difference scheme for the discretization of the nonlinear Poisson–Boltzmann (PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface. The nonlinear PB equation is discretized using finite difference method and several numerical experiments are carried which indicate the second-order accuracy of method. Finally the method is used to study the supercapacitor behaviour of porous electrodes.     

A fourth-order adaptive mesh refinement algorithm for the multicomponent,reacting compressible Navier–Stokes equations

In this paper, we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier–Stokes equations. The algorithm uses a finite-volume approach that incorporates a fourth-order discretisation of the convective terms. The time-stepping algorithm is based on a multi-level spectral deferred corrections method that enables explicit treatment of advection and diffusion coupled with an implicit treatment of reactions. The temporal scheme is embedded in a block-structured adaptive mesh refinement algorithm that includes subcycling in time with spectral deferred correction sweeps applied on levels. Here we present the details of the multi-level scheme paying particular attention to the treatment of coarse–fine boundaries required to maintain fourth-order accuracy in time. We then demonstrate the convergence properties of the algorithm on several test cases including both non-reacting and reacting flows. Finally we present simulations of a vitiated dimethyl ether jet in 2D and a turbulent hydrogen jet in 3D, both with detailed kinetics and transport.     

h-Multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Being implicit in time, the space-time discontinuous Galerkin discretization of the compressible Navier–Stokes equations requires the solution of a non-linear system of algebraic equations at each time-step. The overall performance, therefore, highly depends on the efficiency of the solver. In this article, we solve the system of algebraic equations with a h-multigrid method using explicit Runge–Kutta relaxation. Two-level Fourier analysis of this method for the scalar advection–diffusion equation shows convergence factors between 0.5 and 0.75. This motivates its application to the 3D compressible Navier–Stokes equations where numerical experiments show that the computational effort is significantly reduced, up to a factor 10 w.r.t. single-grid iterations.     

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.     

Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier–Stokes asymptotics

In this paper, we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier–Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of the Boltzmann (or BGK) equation that couples a kinetic equation with macroscopic ones. This new formulation is then discretized with a semi-implicit time scheme combined with a staggered grid space discretization. Finally, several numerical tests are presented in order to illustrate the efficiency of our approach. Incidentally, we also introduce in this paper a modification of a standard splitting method that allows to preserve the compressible Navier–Stokes asymptotics in the case of the simplified BGK model. Up to our knowledge, this property is not known for general collision operators.     

部分相干光束经过湍流大气传输研究进展

相较于相干光束,部分相干光束经过湍流大气传输能够有效地抑制湍流引起的光束展宽、光斑漂移及光强闪烁等扰动效应,在自由空间光通信、激光雷达和激光遥感等方面有重要的应用前景.近年来,部分相干光束湍流大气传输研究受到越来越多学者的关注.本文回顾了部分相干光束在湍流大气中传输特性研究的发展历程、理论基础及常用的理论方法,介绍了处理光束经过湍流大气传输的相位屏数值模拟方法,以及如何把该方法运用到处理部分相干光束传输.     

Influence of turbulent atmosphere on the far-field coherent combined beam quality

Propagation of coherent combined laser beams in turbulent atmosphere is numerically studied based on the extended Huygens-Fresnel principle. By choosing beam propagation factor (BPF) and beam quality factor (BQ) to characterize the far-field irradiance distribution properties, the influence of turbulence on far-field coherent combined beam quality is studied in detail. The investigation reveals that with the coherence length decreasing, the irradiance distribution pattern evolves from typical non-Gaussian shape with multiple side-lobes into Gaussian shape which is seen in the incoherent combining case. In weak turbulent atmosphere, the far-field beam quality suffers less when the 1aser array gets more compact and operates at a longer wavelength. In strong turbulent atmosphere, the far-field beam quality degrades into the incoherent combining case without any relationship with the fill factor and laser wavelength.     

Statistical and coherence effects in nonlinear optical parametric up conversion. I. Coherent interaction

The distinction between coherent and incoherent nonlinear optical interactions is established at the beginning of the paper. In the first part parametric up conversion (PUC) by coherent nonlinear optical mixing of the strong pumping radiation with weak input radiation is treated with respect to statistical properties of generating radiations. The efficiency of PUC is calculated by means of the conserved statistics method. It is shown that the efficiency of PUC depends upon the photon statistics of the strong pumping radiation only, namely, it decreases with increasing fluctuation level in the pumping radiation. The fourth-order statistics of generated sum-frequency radiation is calculated in the first approximation of the iterative solution. The statistics of both generating radiations are projected into the statistical distribution of the resulting sum-frequency radiation in the same way at the beginning of the process.     

Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows

The localized artificial diffusivity method is investigated in the context of large-eddy simulation of compressible turbulent flows. The performance of different artificial bulk viscosity models are evaluated through detailed results from the evolution of decaying compressible isotropic turbulence with eddy shocklets and supersonic turbulent boundary layer. Effects of subgrid-scale (SGS) models and implicit time-integration scheme/time-step size are also investigated within the framework of the numerical scheme used. The use of a shock sensor along with artificial bulk viscosity significantly improves the scheme for simulating turbulent flows involving shocks while retaining the shock-capturing capability. The proposed combination of Ducros-type sensor with a negative dilatation sensor removes unnecessary bulk viscosity within expansion and weakly compressible turbulence regions without shocks and allows it to localize near the shocks. It also eliminates the need for a wall-damping function for the bulk viscosity while simulating wall-bounded turbulent flows. For the numerical schemes used, better results are obtained without adding an explicit SGS model than with SGS model at moderate Reynolds number. Inclusion of a SGS model in addition to the low-pass filtering and artificial bulk viscosity results in additional damping of the resolved turbulence. However, investigations at higher Reynolds numbers suggest the need for an explicit SGS model. The flow statistics obtained using the second-order implicit time-integration scheme with three sub-iterations closely agrees with the explicit scheme if the maximum Courant–Friedrichs–Lewy is kept near unity.     

Output-based space–time mesh adaptation for the compressible Navier–Stokes equations

This paper presents an output-based adaptive algorithm for unsteady simulations of convection-dominated flows. A space–time discontinuous Galerkin discretization is used in which the spatial meshes remain static in both position and resolution, and in which all elements advance by the same time step. Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space. An iterative method based on an approximate factorization is used to solve both the forward and adjoint problems. The output error estimate drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Detection of space–time anisotropy in the localization of the output error is found to be important for efficiency of the adaptive algorithm, and two anisotropy measures are presented: one based on inter-element solution jumps, and one based on projection of the adjoint. Adaptive results are shown for several two-dimensional convection-dominated flows, including the compressible Navier–Stokes equations. For sufficiently-low accuracy levels, output-based adaptation is shown to be advantageous in terms of degrees of freedom when compared to uniform refinement and to adaptive indicators based on approximation error and the unweighted residual. Time integral quantities are used for the outputs of interest, but entire time histories of the integrands are also compared and found to converge rapidly under the proposed scheme. In addition, the final output-adapted space–time meshes are shown to be relatively insensitive to the starting mesh.     

Fidelities of output coherent images produced by photorefractive two-wave mixing

We study theoretically the fidelities of output coherent images in incoherent-to-coherent conversion based on photorefractive two-wave mixing in the presence of an incoherent image-bearing beam. A vector version of the whole beam split step method is developed. The dependencies of the fidelities of output coherent images on geometric and physical parameters such as the incident direction of the beams, the intensity ratios between the beams, and coupling coefficients are investigated in detail. PACS 42.65.Hw     

各向同性紊流能量衰减的大涡模拟

在多重网格驱动的,高效且得到充分验证的有限体积方法的基础上发展了可压缩流大涡模拟的方法.空间离散采用Jameson的中心格式附加二阶和四阶耗散的方法,时间推进则采用了双时间步长的方法.亚格子剪切应力张量和亚格子热通量用Smagorinsky模型进行模拟.通过对各向同性紊流能量衰减的模拟来验证本方法的准确性和高效性,模拟得到的能量谱和紊流动能衰减历程与过滤后的CBC实验数据吻合良好.