Euler solution using adaptive Cartesian grid with a gridless boundary treatment

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.

HYBRID CARTESIAN GRID/GRIDLESS METHOD FOR CALCULATING VISCOUS FLOWS OVER MULTI-ELEMENT AIRFOILS

A hybrid Cartesian grid/gridless method is developed for calculating viscous flows over multi-element airfoils.The method adopts an unstructured Cartesian grid to cover most areas of the computational domain and leaves only small region adjacent to the aerodynamic bodies to be filled with the cloud of points used in the gridless methods,which results in a better combination of the computational efficiency of the Cartesian grid and the flexibility of the gridless method in handling complex geometries.The clouds of points in the local gridless region are implemented in an anisotropic way according to the features of the thin boundary layer of the viscous flows over the airfoils,and the clouds of points at the vicinity of the interface between the grid and the gridless regions are also controlled by using an adaptive refinement technique during the generation of the unstructured Cartesian grid.An implementation of the resulting hybrid method is presented for solving two-dimensional compressible Navier-Stokes(NS)equations.The simulations of the viscous flows over a RAE2822airfoil or a two-element airfoil are successfully carried out,and the obtained results agree well with the available experimental data.

A Preconditioned Gridless Method for Solving Euler Equations at Low Mach Numbers

A preconditioned gridless method is developed for solving the Euler equations at low Mach numbers.The preconditioned system in a conservation form is obtained by multiplying apreconditioning matrix of the type of Weiss and Smith to the time derivative of the Euler equations,which are discretized using agridless technique wherein the physical domain is distributed by clouds of points.The implementation of the preconditioned gridless method is mainly based on the frame of the traditional gridless method without preconditioning,which may fail to converge for low Mach number simulations.Therefore,the modifications corresponding to the affected terms of preconditioning are mainly addressed.The numerical results show that the preconditioned gridless method still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The paper ends with the nearly incompressible flow over a multi-element airfoil,which demonstrates the ability of the method presented for treating flows over complicated geometries.

Application of Gridless Method to Simulation of Compressible Multi-Material Flows

The least-square gridless method was extended to simulate the compressible multi-material flows. The algorithm was accomplished to solve the Arbitrary Lagrange-Euler( ALE) formulation. The local least-square curve fits was adopted to approximate the spatial derivatives of a point on the base of the points in its circular support domain,and the basis function was linear. The HLLC( Harten-Lax-van Leer-Contact) scheme was used to calculate the inviscid flux. On the material interfaces,the gridless points were endued with a dual definition corresponding to different materials. The moving velocity of the interface points was updated by solving the Riemann problem. The interface boundary condition was built by using the Ghost Fluid Method( GFM).Computations were performed for several one and two dimensional typical examples. The numerical results show that the interface and the shock wave are well captured,which proves the effectiveness of gridless method in dealing with multi-material flow problems.

Gridless Variational Bayesian Inference of Line Spectral from Quantized Samples

Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.

Numerical Simulation for the External Combustion of Base-Bleed Projectile Using Gridless Method

The gridless method coupled with finite rate chemistry model is employed to simulate the external combustion flow fields of M864 base bleed projectile. The fluid dynamics process is described by Euler Equation in 2-D axisymmetric coordinate. The numerical method is based on least-square gridless method,and the inviscid flux is calculated by multi-component HLLC( Harten-Lax-van Leer-Contact) scheme,and a H2-CO reaction mechanism involving 9 species and 11 reactions is used. The computations are performed for the full projectile configuration of Ma = 1. 5,2,and 3. The hot air injection cases and inert cases are simulated for comparison. The numerical results show that due to the combustion in the weak region,the recirculation zone enlarges and moves downstream,the base pressure increases and the total drag force coefficient decreases. At Ma = 3. 0,the rear stagnation point shifts downstream approximate 0. 26 caliber,and the base pressure increases about 53. 4%,and the total drag force coefficient decreases to 0. 182 which agrees well with the trajectory model prediction. Due to neglecting the effects of viscosity and turbulence,there exists a certain difference at Ma = 1. 5,2. 0.

Underwater acoustic multipath sparse channel estimation via gridless relevance vector machine method

In the scenario of underwater acoustic sparse channel estimation with training sequences,grid points in the measuring matrix are caused by discretizing procedure.Estimated accuracy might not be guaranteed with the state-of-the-art methods when multipath delays don't exactly locate on the grid points.In this paper,we construct a gridless measuring matrix for sparse channel estimation which contains an off-grid adjusting factor.The Relevance Vector Machine(RVM) algorithm is employed to estimate this factor.The numerical experiments for two different underwater channels are performed to testify the newly proposed method.The results demonstrate that this method outperforms conventional ones in terms of estimating error and bit error rate,especially when the grid gets coarser.

A Yield-Driven Gridless Router

A new gridless router to improve the yield of IC layout is presented. The improvement of yield is achieved by reducing the critical areas where the circuit failures are likely to happen. This gridless area router benefits from a novel cost function to compute critical areas during routing process, and heuristically lays the patterns on the chip area where it is less possible to induce critical area. The router also takes other objectives into consideration, such as routing completion rate and nets length. It takes advantage of gridless routing to gain more flexibility and a higher completion rate. The experimental results show that critical areas are effectively decreased by 21% on average while maintaining the routing completion rate over 99%.

Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers

In this paper,preconditioned gridless methods are developed for solving the threedimensional(3D)Euler equations at low Mach numbers.The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations,which are discretized under the clouds of points distributed in the computational domain by using a gridless technique.The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning,which may fail to have convergence for flow simulations at low Mach numbers,therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper.An explicit four-stage Runge–Kutta scheme is first applied for time integration,and the lower-upper symmetric Gauss-Seidel(LU-SGS)algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence.Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform,and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing.The gridless clouds of both regular and irregular points are used in the simulations,which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries.Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature.The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally,for nearly incompressible flow simulations at low Mach numbers as well.The convergence of the implicit preconditioned gridless method,as expected,is much faster than its explicit counterpart.

页岩气藏两相流固耦合无网格数值模拟

针对页岩气藏受两相复杂流动与流固耦合作用影响导致产能预测难度大的问题,将渗流场分为主改造区、次改造区和未改造区,结合多流态统一输运模型及等效连续非均匀介质物理模型,建立多尺度气-水两相流动流固耦合数学模型,并利用无网格广义有限差分法对数学模型进行编程求解。研究结果表明:无网格广义有限差分法能适应不同计算域情况,避免传统差分网格与非结构网格耦合所导致的运算不稳定;压降前缘在未改造区的传播仅为20 m左右,固体位移主要发生在次改造区与未改造区的交界区域;忽略应力场的影响,气井投产初期产气量被显著高估,到生产后期这种影响逐渐下降;低初始含水饱和度的页岩气藏更有益于开发,储层优选时应重点考虑含水饱和度。研究成果对流固耦合数值模拟及非常规油气藏产能预测具有指导意义。

低信噪比下非冗余阵列的无网格DOA估计

波达方向(direction of arrival,DOA)是阵列信号处理模型中的非线性参数,当信噪比较低时,其估计值会偏离真实值。为了降低无网格DOA估计方法中该问题的阈值,介绍了一种基于无网格的基于协方差的稀疏迭代估计(sparse iterative covariance-based estimation,SPICE)方法。引入了最大似然求根多重信号分类(maximum likelihood root multiple signal classification,ML-Root-MUSIC)来计算DOA,使用最大似然准则来选择根,可以降低阈值并获得更好的分辨率特性。在原始无网格SPICE的优化问题中加入了负熵项,使得无网格SPICE的均方根误差曲线更接近于Cramer-Rao下界。最后,蒙特卡罗仿真实验验证了所提方法在低信噪比非冗余阵列情况下的优越性。

基于ANM的非均匀圆阵二维DOA估计

传统的基于原子范数最小化(Atomic Norm Minimization,ANM)的波达方向(Direction of Arrival,DOA)估计算法无法直接应用于不满足范德蒙德结构的非均匀圆阵,针对这一问题提出了一种基于虚拟阵列变换的改进方法。以某非均匀圆阵作原始阵列为例,首先通过虚拟阵列变换处理原始阵列接收的数据,使其转换为虚拟的均匀L阵接收数据,将非均匀圆阵上的DOA估计问题转化为两个均匀线阵上的DOA估计问题,再利用基于ANM的DOA估计算法与L型阵的二维角度关系还原出方位角和俯仰角。通过仿真与实测实验验证了所提算法应用于非均匀圆阵的可行性,并分析其DOA估计结果,证明其拥有较高的估计精度。

稀疏恢复空时自适应处理技术研究综述

相较于传统空时自适应处理(STAP)技术,稀疏恢复(SR)STAP技术在小样本条件下杂波抑制性能显著提升,因此适用于现实非均匀杂波环境.本文首先阐述了SR STAP基本原理,分析了机载雷达杂波空时稀疏特性;然后总结了SR STAP发展历史与现状,并在此基础上针对其相关科学问题进行了探讨,包括:空时谱估计还是杂波抑制、单观测样本还是多观测样本、白化还是置零、重构算法参数依赖还是不依赖、非平稳杂波下是否适用及干扰条件下是否可行;最后给出了当前SR STAP技术走向实用化过程中所面临的关键问题,即网格失配和空域误差影响,并分别讨论了无网格压缩感知和字典自校正的解决途径.

如何解决基不匹配问题:从原子范数到无网格压缩感知

压缩感知理论能够以远低于经典Nyquist速率进行采样,采用非自适应线性投影获得了保留信号有用信息的少量观测点,并通过求解最优化问题精确重构原始信号.压缩感知理论大大缓解了信号采样、存储和传输的巨大压力,在计算机科学、电子工程和信号处理等领域具有广阔的应用前景.信号的稀疏表示是对信号进行压缩采样和重构的前提,即假设信号在某个变换基(傅里叶基、小波基等)下是稀疏的,这些基可以看作是用于描述信号参数空间的有限离散字典.然而在如雷达、阵列信号处理、通信等领域的应用中,信号的参数空间是连续的,在假定的离散变换基下并不稀疏,这种基不匹配问题会严重影响信号重构精度.本文首先介绍了基不匹配产生的原因及其对重构精度的影响,接着从原子范数出发,综述了无网格压缩感知的理论框架和关键技术问题,着重介绍了一维和多维无网格压缩感知的最新研究进展,最后对其在信号处理等领域的应用进行了探讨.

高雷诺数下求解NS方程的无网格算法

提出了一种适合高雷诺数NS方程求解的隐式无网格算法。针对高雷诺数粘性流动的特点,在附面层内的粘性影响区域采用法向层次推进布点的方法形成离散点云,在附面层外的计算区域内实行填充式布点的方法形成离散点云。根据附面层内外点云的不同构造特点,推导出运用格林公式和最小二乘曲面拟合方法求取空间导数的统一形式,在此基础上运用AUSM+_up格式求得数值通量,并引入BL湍流模型对雷诺平均NS方程的湍流应力项进行封闭。时间推进格式方面,采用了计算效率较高的隐式高斯-赛德尔迭代算法。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型低速流动、RAE2822翼型跨音速绕流和二维圆柱的分离流动进行了数值模拟。

动边界问题无网格算法及其动态点云

提出基于Delaunay图映射的点云运动处理技术。该技术使点云随物体运动再生成问题变成简单的映射关系,无需迭代,且能保持点云结构不变,故有效地避免了因点云结构变动而产生的附加计算量。运用该技术,结合非定常Euler方程双时间步无网格算法,成功地模拟了翼型的跨声速非定常流动。其中物理时间迭代采用二阶隐式格式,伪时间迭代采用四步龙格-库塔显式格式。文中给出了不同翼型的计算结果,并与实验结果进行了比较,取得了令人满意的结果。

AUSM^+-up格式在无网格算法中的推广

将AUSM+-up格式推广运用到了无网格算法中。在点云离散的基础上,运用曲面拟合和AUSM+-up格式求得数值通量;采用四步龙格-库塔方法进行时间推进,并引入当地时间步长和残值光顺等加速收敛措施。为了验证本文方法的计算精度和鲁棒性,对NACA0012翼型跨声速流动、某三段翼型低速绕流、平行错位NACA0012双翼超声速、高超声速流动进行了数值模拟。

含化学反应膛口流场的无网格数值模拟

基于无网格方法,对包含大位移运动边界和非平衡化学反应的膛口流场进行了数值模拟。所发展算法是基于线性基函数最小二乘显式无网格方法,忽略黏性及湍流的影响,对流场采用ALE(arbitrary Lagrangian-Eulerian)形式的Euler方程描述,对流通量和化学反应源项采用多组分HLLC(Harten-Lax-van Leer-Contact)格式和有限速率反应模型计算,对于运动边界造成的点云畸形采用局部点云重构方法处理,重构过程中采用虚拟边阵面推进。对圆柱绕流和激波诱导燃烧流场进行了数值模拟,验证了重构方法和化学反应计算的有效性。最后对12.7mm口径机枪膛口流场进行了模拟,结果同实验照片、非结构网格方法结果吻合较好,数值结果清晰地再现了膛口初始冲击波、膛口冲击波、欠膨胀射流波系结构的动力学发展过程,以及膛口焰的时间、空间分布特征。

基于Riemann解的二维流体力学Lagrange有限点无网格方法

在高维流体力学计算中,对于多介质大变形等一类问题,采用有网格方法常遇到较大的困难.针对二维问题,研究了一种无网格方法———Lagrange有限点方法:在求解区域上设置适当的离散点集,视其中每一点为流体力学Lagrange点;对于点集的任一点,确定邻点集合,并基于该点同邻点集合的联系,应用Godunov方法将流体力学Lagrange方程进行离散;考虑到算法的稳健性,方法中可设置较多邻点并采用最小二乘法.将该方法应用于典型的数值算例,取得了良好效果.