| 1. | Analysis of the accuracy of the spatial discretization schemes for surface integrals in finite volume method
有限体积法中面积分离散格式的精度分析 |
| 2. | The 3rd - order splitting algorithm based on the mixed stiffly stable scheme is employed in the temporal discretization of the n - s equations and the mixed fourier - spectral - spectral - element method in the spatial discretization
Navier - stokes方程的时间离散采用基于混合刚性稳定格式的三阶分裂算法，空间离散采用fourier谱谱元法。 |
| 3. | The accuracies of the different orders symplectic difference schemes are compared and the effect of the spatial discretization methods upon the accuracy is analyzed by simulating the propagation of a one - dimensional wave under the periodic boundary condition
本文用一维波动方程的初边值问题初步比较了不同阶数辛格式的精度，并分析了空间离散格式对精度的影响。 |
| 4. | 3 . high order weno scheme in spatial discretization and 3rd order tvd runge - kutta schemes in time stepping were used to time - dependent hamilton - jacobi type equation , in order to improve calculation precision . the resultes show the precision is improved obviously and no oscillation appear . 4
求解等值面函数法的控制方程时，空间离散采用了高分辨率的weightedeno格式，时间离散采用3阶tvdrunge - kutta方法，解决了数值震荡的问题，提高了计算精度； 4 |
| 5. | Compared with octree data structure , the omni - tree data structure could reduce the meshes " total numbers and get better mesh quality . this paper uses cell - centered finite volume spatial discretization and four - stage runge - kutta time - stepping scheme with some convergence acceleration techniques such as local time stepping and enthalpy damping
在流场计算中，本文采用格心格式的有限体积法用二阶中心差分对欧拉方程作空间离散，用四步龙格库塔方法作显式时间推进。 |
| 6. | The fourth - order explicit upwind - biased compact difference schemes are used in the spatial discretization of the nonlinear convection terms . these difference schemes can be used in all computational region including the boundary neighborhood , and can overcome the difficulty not adapting simultaneously in the boundary neighborhood for general three - dimensional fourth - order central difference schemes , and improve computational stability a nd resolution . the compact difference equations with high accuracy and resolution for solving the incompressible n - s equations and perturbation equations are composed of these compact difference schemes , and provides an effective numerical method for the investigations of the turbulent spots and coherent structures
文中发展了四阶时间分裂法用于navier - stokes方程及其扰动方程的时间离散；对分裂得出的关于压力的poisson方程和关于速度的helmholtz方程，建立三维耦合四阶紧致迎风差分格式；这些格式适用于包括邻近边界点在内的计算区域，克服了三维各自用四阶中心差分格式离散不适用于边界邻域的困难，并提高了稳定性和分辨率，用这些格式分别组成了数值求解navier - stokes方程及其扰动方程的高精度、高分辨率的紧致差分方程组，为湍斑及湍流相干结构的研究提供了有效的数值方法。 |
| 7. | The main numerical method of this code is coming from scheme ( jameson , schimit and turkel ) : using cell - centered finite volume method as spatial discretization tools , and a system of ordinary differential equations for time variable is obtained , which is solved by utilizing five - step runge - kutta scheme as time marching method , introducing artificial dissipation to damp high frequency oscillations near the shock and stagnation point
本论文采用欧拉方程作为控制方程，利用中心有限体积法进行空间离散，得到对时间变量的常微分方程组，采用龙格库塔多步法进行时间积分，加入人工粘性以消除激波和驻点附近的压力振荡等方法来对naca0012翼型的实际流动进行并行数值模拟。 |
| 8. | In this paper , the upwind scheme and the central scheme are presented for solving 3 - d n - s equations using the cell - center finite volume spatial discretization and four - stage runge - kutta time stepping scheme , with standard convergence acceleration techniques such as local time stepping and implicit residual smoothing
在n - s方程的数值计算上，采用了中心差分格式和迎风格式，用格心格式的有限体积法进行了空间离散，用四步龙格?库塔法作显式时间推进，并采用了当地时间步长和隐式残差光顺等加速收敛措施。 |
| 9. | By use of - perturbation method with spatial discretization , the hydraulic transient system controlled by quasilinear partial differential equation was converted to a time - continuous linear system , so that the inverse problem of hydraulic transients under limited pressure could be sol ed with the optimal control theory for time - continuous systems
采用-摄动法并经过空间离散，将由拟线性偏微分方程控制的有压瞬变流系统转化为时间连续线性系统，从而使有压瞬变流限压控制反问题能应用时间连续系统最优控制理论来求解。 |
