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(shí)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(dòng)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(duì)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(shí),空間離散采用了高分辨率的weightedeno格式,時(shí)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(jì)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(chǎng)計(jì)算中,本文采用格心格式的有限體積法用二階中心差分對(duì)歐拉方程作空間離散,用四步龍格庫塔方法作顯式時(shí)間推進(jìn)。
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(shí)間分裂法用于navier - stokes方程及其擾動(dòng)方程的時(shí)間離散;對(duì)分裂得出的關(guān)于壓力的poisson方程和關(guān)于速度的helmholtz方程,建立三維耦合四階緊致迎風(fēng)差分格式;這些格式適用于包括鄰近邊界點(diǎn)在內(nèi)的計(jì)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(dòng)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(gòu)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(jìn)行空間離散,得到對(duì)時(shí)間變量的常微分方程組,采用龍格庫塔多步法進(jìn)行時(shí)間積分,加入人工粘性以消除激波和駐點(diǎn)附近的壓力振蕩等方法來對(duì)naca0012翼型的實(shí)際流動(dòng)進(jìn)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(jì)算上,采用了中心差分格式和迎風(fēng)格式,用格心格式的有限體積法進(jìn)行了空間離散,用四步龍格?庫塔法作顯式時(shí)間推進(jìn),并采用了當(dāng)?shù)貢r(shí)間步長(zhǎng)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(dòng)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(shí)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(yīng)用時(shí)間連續(xù)系統(tǒng)最優(yōu)控制理論來求解。