三维对流扩散方程非等距网格上的四阶紧致格式及其多重网格方法

提出了数值求解三维变系数对流扩散方程非等距网格上的四阶精度19点紧致差分格式,为了提高求解效率,采用多重网格方法求解高精度格式所形成的大型代数方程组。数值实验结果表明本文方法对于不同的网格雷诺数问题,在精确性、稳定性和减少计算工作量方面均明显优于7点中心差分格式。     

气相爆轰高阶中心差分-WENO组合格式自适应网格方法

研究一种高阶中心差分-WENO组合格式,并采用自适应网格方法进行二维和三维气相爆轰波的数值模拟.采用ZND爆轰模型的控制方程为包含化学反应源项的Euler方程组.组合格式在大梯度区采用WENO格式捕捉间断,在光滑区采用高阶中心差分格式提高计算效率.采用一种基于流场结构特征的自适应网格.计算结果,表明这种方法同时具有高精度、高分辨率和高效率的特点.     

四阶紧致差分格式对静力模式中垂直网格计算频散性的影响

为了说明四阶紧致差分格式在大气和海洋数值模式中的潜在价值,提出一种通用方法,推导静力线性斜压适应方程组在微分和差分情况下的频散关系,水平尺度分100 km,10 km和1 km三种情况,从频率、水平群速和垂直群速方面,对采用二阶中央差和四阶紧致差分格式情况下,非跳点网格(N网格)、Lorenz网格(L网格)、Charney-Phillips网格(CP网格)、Lorenz时间跳点网格(LTS网格)和Charney-Phillips时间跳点网格(CPTS网格)的计算特性进行比较,发现采用高精度的四阶紧致差分格式总体上可以明显减少上述三种水平尺度波动在N网格、CP网格、L网格和CPTS网格上的频率、水平群速和垂直群速误差,但对LTS网格,采用四阶紧致差分格式,会使得计算水平群速和垂直群速误差变大.     

跨音速S形进气道内外流场的混合差分计算

提出了一种计算跨音速S形进气道内外流场的混合差分方法.该法从速势方程出发,利用直角和圆柱坐标系、不旋转的混合差分格式以及边界的解析延拓处理,建立了流场内各网格点的差分方程,并用线松弛法进行统一迭代.计算了一个S形进气道在来流马赫数为0.8以及不同攻角状态下的内外流场,并将计算结果与摄动法计算结果以及实验值进行了比较.     

高精度格式WCNS-E-5计算物面热流

采用加权紧致非线性格式WCNS-E-5,四阶精度的二阶导数差分近似以及四阶精度的边界格式构造了高精度算法,对高超声速粘性流动的物面热流进行数值研究.首先考察了壁面网格雷诺数对驻点热流的影响,然后开展了边界格式对热流计算结果影响的研究,最后对大攻角钝锥绕流进行了数值模拟.研究结果表明:WCNS-E-5能降低边界层内网格分辨率,全场高精度的WCNS-E-5计算得到的流场图像清晰、真实、分辨率高,热流值准确、可靠.     

保持对称性的二维Lagrange流体力学有限差分方法

广泛应用的二维直角坐标系下的Wilkins有限差分格式在计算一维柱面问题时,通过等角度划分周向网格能够获得严格的对称性,非等角度划分周向网格会产生较严重的不对称性.通过分析Wilkins有限差分格式在处理非等角度划分周向网格的一维柱面问题时破坏对称性的原因,指出周向网格的非等角度划分产生了周向压力分量,从而产生了周向加速度分量和周向运动速度,以此为基础提出一种对该有限差分格式进行修正的方法,将节点处的周向压力分量做算术平均运算,以消除周向压力分量,只剩径向压力分量起作用.因而该修正方法在以任意角度划分周向网格的条件下都能够保持严格的对称性.通过几个典型算例验证该结论,对对称流动,修正方法与原始方法所获得的结果一致,对非对称流动,二者有微小差异.     

基于气动声学问题的高阶非线性紧致格式

文章基于线性中心紧致差分格式, 通过非线性加权插值的方法来求解网格中心处的函数值.这类格式保持了原有中心紧致差分格式的高阶精度和低耗散特性, 同时其分辨率也非常高, 由于其非线性插值的机制, 使得这类格式能够捕捉强激波, 所以这类新的高阶非线性紧致格式是一种较好的模拟湍流和气动声学等多尺度问题的方法.      

高精度有限差分在湍流直接数值模拟中的应用

本文采用高精度有限差分法对矩形管道内充分发展湍流换热进行了直接数值模拟,湍流雷诺数Rer和普朗特数分别为400(Rem=6200)和0.71,压力泊松方程分别采用两种不同的离散格式(二阶和四阶中心差分离散).结果表明,同二阶中心差分格式相比,高精度有限差分可以在较少的网格下得到较好的结果;压力泊松方程采用四阶中心差分或二阶中心差分对计算结果的影响甚小,但采用二阶中心差分时,可以节省大量的计算时间.     

基于变分原理的二维热传导方程差分格式

研究二维热传导方程的差分数值模拟.用变分原理在不规则结构网格上建立热流通量形式的差分格式.将热流通量作为未知函数求泛函极值,并与温度函数联立求解.克服通常九点格式用插值方法计算网格边界上的热传导系数和网格结点上的温度所引入的误差.     

一种求解可压缩Navier-Stokes方程的隐式迭代时间推进方法

针对有壁面边界的可压缩流动问题,提出与基于非等距网格的高精度紧致型差分格式相结合的简化隐式迭代时间推进法,建立求解可压缩Navier-Stokes方程的直接数值模拟方法,提高了计算效率.应用该方法,直接数值模拟两种有壁面边界的二维可压缩流动问题,即可压缩平板边界层流动和可压缩槽道流动.     

BOR-FDTD subgridding based on finite element principles

In this paper a recently developed provably passive and stable 3D FDTD subgridding technique, based on finite elements principles, is extended to body-of-revolution (BOR) FDTD. First, a suitable choice of basis functions is presented together with the mechanism to assemble them into an overall mesh consisting of coarse and fine mesh cells. Invoking appropriate mass-lumping concepts then leads to an explicit leapfrog time stepping algorithm for the amplitudes of the basis functions. Attention is devoted to provide the reader with insight into the updating equations, in particular at a subgridding boundary. Stability, grid reflection and dispersion are also discussed. Finally, some numerical examples for toroidal and cylindrical cavities demonstrate the stability and accuracy of the method.     

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma = 6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at freestream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibility effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely tO OCCUr.     

A novel mesh regeneration algorithm for 2D FEM simulations of flows with moving boundary

A novel mesh regeneration algorithm is proposed to maintain the mesh structure during a finite element simulation of flows with moving solid boundary. With the current algorithm, a new body-fitted mesh can be efficiently constructed by solving a set of Laplace equations developed to specify the displacements of individual mesh elements. These equations are subjected to specific boundary conditions determined by the instantaneous body motion and other flow boundary conditions. The proposed mesh regeneration algorithm has been implemented on an arbitrary Lagrangian–Eulerian (ALE) framework that employs an operator-splitting technique to solve the Navier–Stokes equations. The integrated numerical scheme was validated by the numerical results of four existing problems: a flow over a backward-facing step, a uniform flow over a fixed cylinder, the vortex-induced vibration of an elastic cylinder in uniformly incident flow, and a complementary problem that compares the transient drag coefficient for a cylinder impulsively set into motion to that measured on a fixed cylinder in a starting flow. Good agreement with the numerical or experimental data in the literature was obtained and new transient flow dynamics was revealed. The scheme performance is further examined with respect to the parameter employed in the mesh regeneration algorithm.     

A High-Order Discontinuous Galerkin Method for the Two-Dimensional Time-Domain Maxwell's Equations on Curved Mesh

In this paper, a DG (Discontinuous Galerkin) method which has been widely employed in CFD (Computational Fluid Dynamics) is used to solve the two-dimensional time-domain Maxwell's equations for complex geometries on unstructured mesh. The element interfaces on solid boundary are treated in both curved way and straight way. Numerical tests are performed for both benchmark problems and complex cases with varying orders on a series of grids, where the high-order convergence in accuracy can be observed. Both the curved and the straight solid boundary implementation can give accurate RCS (Radar Cross-Section) results with sufficiently small mesh size, but the curved solid boundary implementation can significantly improve the accuracy when using relatively large mesh size. More importantly, this CFD-based high-order DG method for the Maxwell's equations is very suitable for complex geometries.     

Modeling slender bodies with the method of regularized Stokeslets

The motion and flow generated by immersed structures in a fluid in the Stokes regime can be modeled with a variety of different numerical methods. The mathematical structure of the Stokes equations allows one to describe the flow around a three-dimensional object using only information regarding its geometry. This leads to computational techniques such as boundary integral methods or the method of regularized Stokeslets that discretize the surface of the immersed object in the flow. However, when the body in question is slender, a more computationally efficient alternative is to represent the flow by a one-dimensional discretization along the centerline of the object rather than a discretization of the boundary. Using an exact and an asymptotic solution describing the nontrivial three-dimensional fluid flow generated by a slender precessing spheroid, we present a careful analysis of the approximation of the flow using the method of regularized Stokeslets, where the regularized Stokeslets are placed along the centerline of the spheroid. Guidance is presented on how best to choose the numerical parameters within the method of regularized Stokeslets to minimize the error for a given application.     

Investigation of piezoelectrically generated synthetic jet flow

The purpose of this paper is to investigate the compressible turbulent synthetic jet flow characteristics of a dual diaphragm piezoelectric actuator. Experimentally, a flow visualization system was established to obtain the particle streak images scattered from 10-μm red fluorescent spheres for observing the synthetic jet flowfield produced by a dual diaphragm piezo actuator. The centerline velocity of the synthetic jet was also measured by using a hot-wire anemometry system. In the analysis, the computational approach adopted the transient three-dimensional conservation equations of mass and momentum with the moving boundary specified to represent the piezo diaphragm motion. The standard k-∈ two-equation turbulent model was employed for turbulence closure. For the actuator operating at the frequency of 648 Hz, the particle streakline images in the cross-sectional plane visualized a turbulent jet flow pattern in the far-field area. The hot-wire anemometry data indicated that the measured centerline velocity of synthetic jets reached 3.8 m/s at y/d= 50. The predictions were compared with the visualized particle streak images and centerline velocity of the synthetic jet in order to validate the computer code. The numerical simulation revealed the time-periodic formation and advection of discrete vortex pairs. Caused by the outward movement of the piezo diaphragms, air near the orifice was entrained into the actuator cavity when the vortex pairs were sufficiently distant from the orifice.     

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

A lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.     

Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

This article considers a posteriori error estimation and anisotropic mesh refinement for three-dimensional laminar aerodynamic flow simulations. The optimal order symmetric interior penalty discontinuous Galerkin discretization which has previously been developed for the compressible Navier–Stokes equations in two dimensions is extended to three dimensions. Symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model. Using duality arguments, an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients. Furthermore, residual-based indicators as well as adjoint-based indicators for goal-oriented refinement are derived. These refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous Galerkin (DG) discretization. Two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint-based error estimation are presented. The performance of the proposed discretization, error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows.     

A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows

A momentum exchange-based immersed boundary-lattice Boltzmann method is presented in this Letter for simulating incompressible viscous flows. This method combines the good features of the lattice Boltzmann method (LBM) and the immersed boundary method (IBM) by using two unrelated computational meshes, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid boundaries in the flow. In this method, the non-slip boundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation (LBE). Unlike the conventional IBM using the penalty method with a user-defined parameter or the direct forcing scheme based on the Navier–Stokes (NS) equations, the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. Numerical examples show that the present method can provide very accurate numerical results.     

稳态问题混合边界积分方程的高精度求积法与分裂外推

提出了求积法解稳态问题的混合边界积分方程,它拥有高精度,低复杂度.通过并行地解粗网格上的离散方程,根据误差的多参数渐近展开,应用分裂外推算法得到高精度的近似解,同时获得后验误差估计.