Analysis of the accuracy of the spatial discretization schemes for surface integrals in finite volume method 有限體積法中面積分離散格式的精度分析
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方程的時間離散采用基于混合剛性穩(wěn)定格式的三階分裂算法,空間離散采用fourier譜譜元法。
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 本文用一維波動方程的初邊值問題初步比較了不同階數(shù)辛格式的精度,并分析了空間離散格式對精度的影響。
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 求解等值面函數(shù)法的控制方程時,空間離散采用了高分辨率的weightedeno格式,時間離散采用3階tvdrunge - kutta方法,解決了數(shù)值震蕩的問題,提高了計算精度; 4
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 在流場計算中,本文采用格心格式的有限體積法用二階中心差分對歐拉方程作空間離散,用四步龍格庫塔方法作顯式時間推進。
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 文中發(fā)展了四階時間分裂法用于navier - stokes方程及其擾動方程的時間離散;對分裂得出的關于壓力的poisson方程和關于速度的helmholtz方程,建立三維耦合四階緊致迎風差分格式;這些格式適用于包括鄰近邊界點在內(nèi)的計算區(qū)域,克服了三維各自用四階中心差分格式離散不適用于邊界鄰域的困難,并提高了穩(wěn)定性和分辨率,用這些格式分別組成了數(shù)值求解navier - stokes方程及其擾動方程的高精度、高分辨率的緊致差分方程組,為湍斑及湍流相干結(jié)構的研究提供了有效的數(shù)值方法。
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 本論文采用歐拉方程作為控制方程,利用中心有限體積法進行空間離散,得到對時間變量的常微分方程組,采用龍格庫塔多步法進行時間積分,加入人工粘性以消除激波和駐點附近的壓力振蕩等方法來對naca0012翼型的實際流動進行并行數(shù)值模擬。
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方程的數(shù)值計算上,采用了中心差分格式和迎風格式,用格心格式的有限體積法進行了空間離散,用四步龍格?庫塔法作顯式時間推進,并采用了當?shù)貢r間步長和隱式殘差光順等加速收斂措施。
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-攝動法并經(jīng)過空間離散,將由擬線性偏微分方程控制的有壓瞬變流系統(tǒng)轉(zhuǎn)化為時間連續(xù)線性系統(tǒng),從而使有壓瞬變流限壓控制反問題能應用時間連續(xù)系統(tǒng)最優(yōu)控制理論來求解。