可压缩各向同性衰减湍流直接数值模拟研究

采用五阶有限差分WENO格式直接模拟了高初始湍流Mach数的可压缩均匀各向同性湍流,主要分析了湍流的统计特性 和压缩性的影响,包括能谱特征、激波串、耗散率、标度律等. 研究表明,湍动能主要来自于速度场螺旋分量的贡献;各向同性湍流的小尺度脉动对压缩性更为敏感,并且压缩性的增强加快了湍流大 尺度脉动向小尺度脉动的湍动能输运;随着湍流Mach数的升高,胀量(压缩)耗散率所占比率也显著增长. 标度律分析表明,强可压缩湍流的横向速度结构函数仍然具有扩展自相似性;当阶数较高(p ≥ 5)时,纵向速度结构函数的扩展自相似性则不再成立. 对于压缩性较弱的湍流,与不可压缩湍流一致,横向湍流脉动的间歇性要强于纵向湍流脉动;而对于强可压缩湍流,纵向湍流脉动的 间歇性要强于横向湍流脉动.  

基于HLL-HLLC的高阶WENO格式及其应用研究

HLL-HLLC格式能够克服HLLC在强激波附近的激波不稳定现象，并且保持了HLLC的低耗散特性，是一种适合更大马赫数范围的近似黎曼求解器。本文从RANS方程出发，将HLL-HLLC近似黎曼求解器结合五阶WENO重构，实现了对无粘通量的高阶离散；同时，采用完全守恒形式的四阶中心差分格式处理粘性项，建立了RANS 方程的高阶数值求解格式。通过对四个经典算例，钝头体、 ONERA M6机翼、DLR F6-WB翼身组合体和DLR F6-WBNP复杂外形的数值模拟，考察了两种WENO改进格式在复杂流场中的表现，研究了高阶格式的收敛特性；给出了在复杂流动中 WENO自由参数的推荐值，以增强求解的收敛性。算例结果表明，本文构造的高阶格式鲁棒性好，能够显著改善激波位置和激波强度，捕获更丰富的流场细节，满足复杂工程应用需求。  

加权型紧致格式与加权本质无波动格式的比较

线性紧致格式和加权本质无波动格式是两种典型的高阶精度数值格式,它们各有优缺点.线性紧致格式在具有高阶精度的同时,格式的分辨率也比较高,耗散低,是计算多尺度流场结构的较好格式,但是不能计算具有强激波的流场.加权本质无波动格式是一种高阶精度捕捉激波格式,鲁棒性好,但耗散比较高,分辨率也不理想.近年来,在莱勒的线性紧致格式基础上,采用加权本质无波动格式捕捉激波思想,发展了一系列加权型紧致格式.本文较全面地比较了加权型紧致格式和加权本质无波动格式,包括构造方法、鲁棒性、分辨率、耗散特性、收敛特性以及并行计算效率.结果表明,现有的加权型紧致格式基本保持了加权本质无波动格式的性质,对于气动力等宏观量的计算,比加权本质无波动格式没有明显的优势.  

利用多小波自适应格式求解流体力学方程

高阶计算格式的高精度、高分辨率对提高复杂流场的计算水平有重要的意义， 为了提高AUSMPW格式对流场计算中激波等间断的分辨率，减小数值振荡，在原有AUSMPW 格式的基础之上，利用多小波对函数进行多尺度分解，并采取阈值的方法生成自适应网格， 提出了一种新的基于多小波自适应算法的AUSMPW格式，理论上可以达到任意阶精度. 将所得 的压强、密度与原格式、TVD格式及WENO格式的计算结果进行了比较分析. 结果表明改进后 的AUSMPW格式较原格式具有更高的分辨率、更强的捕捉间断的能力及更低的数值耗散.  

T型管内流动气体中爆轰绕射过程的数值模拟

基于带化学反应的二维Euler方程,对H2、O2、Ar体积比为2∶1∶1的混合气体系统在T型管内的爆轰绕射进行了数值模拟。用二阶附加半隐的Runge-Kutta法和五阶WENO格式分别离散欧拉方程的时间和空间导数项,采用9组分48步基元反应简化模型描述爆轰波在静止系统和流动系统中的传播过程,得到了温度、压力、典型组元H质量分数的分布及数值胞格结构。结果表明:在流动系统中,迎风面上波阵面为斜爆轰结构,静止系统两侧和顺风面上的波阵面为完全解耦的前导激波;在水平管中,波阵面与上下壁面经历一系列马赫碰撞后,最终形成正爆轰;在流动系统中,胞格结构明显向下游偏移;横向爆轰波的产生对爆轰波的再生起到了关键作用。  

复杂地形条件下WENO-Roe方法在浅水模拟中的改进

在分析浅水方程与二维空气运动方程差异的基础上,在不改变原有浅水方程形式的前提下,提出了局部水位法离散连续方程,并针对动量方程中底坡项提出了更具普遍意义的离散方法,保证了浅水方程离散后的平衡性。通过不规则地形下潮流以及混合流流动的模拟,得到的计算结果符合物理实际,与精确解符合良好,最大相对误差不超过4%,验证了此方法在复杂地形上的平衡性,同时本方法又具有良好的间断捕捉能力与稳定性。  

Characteristic-based finite volume scheme for 1D Euler eouations

In this paper, a high-order finite-volume scheme is presented for the one-dimensional scalar and inviscid Euler conservation laws. The Simpson's quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson's quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.  

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomials,termed as HWENO schemes,is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids.The developed HWENO methodology utilizes high-order derivative information to keep WENO reconstruction stencils in the von Neumann neighborhood.A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils,making higher-order scheme stable and simplifying the reconstruction process at the same time.The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement.Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy,the designed HWENO limiters can simultaneously obtain uniform high order accuracy and sharp,essentially non-oscillatory shock transition.  

Characteristic-based finite volume scheme for 1D Euler equations

In this paper, a high-order finite-volume scheme is presented for the one- dimensional scalar and inviscid Euler conservation laws. The Simpson＇s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson＇s quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory （CWENO） reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.  

Problem-independent nonlinear switch for newly designed WENO-BO-Z scheme

The uniformly third-order WENO-BO-Z scheme has been proposed previously in an attempt to restore third-order accuracy at the second-order critical point via the reduction of nonlinear dissipation followed by the modification of nonlinear weights as well as to improve the intermediate bandwidth property of the linear optimal stencil of the classical WENO-JS scheme with respect to both dispersion and dissipation. However, a problem-dependent nonlinear switch was employed to turn on in the intermediate range of wavenumbers to avoid unnecessary nonlinear adaption of the WENO scheme and was mainly dependent on the trial-and-error threshold value of a switch parameter. In order to avoid the problem-dependent nature of this switch, a problem-independent nonlinear switch is suggested and investigated in this work. Benchmark problems, ranging from non-broadband to broadband, are solved using the WENO-BO-Z scheme, and a comparison of the suggested switch with the problem-dependent switch is made.