Convergence is accelerated by means of local time stepping , implicit residual smoothing . the numerical results have been obtained for the flows over n ac ago 12 or rae2822 airfoils 并且基于點(diǎn)云離散結(jié)構(gòu),引入了當(dāng)?shù)貢r(shí)間步長(zhǎng)、殘值光顧等加速收斂技術(shù),數(shù)值模擬了對(duì)稱和非對(duì)稱翼型繞流,獲得較好的計(jì)算結(jié)果。
In order to accelerate the convergence , residual smoothing and local time stepping were employed . in the same time , by improving prolongation operator , a new multi - grid scheme which can combine well with the algorithm of this thesis 為加速計(jì)算收斂速度,除了采用當(dāng)?shù)貢r(shí)間步長(zhǎng)和局部殘差光順技術(shù)外,通過改造插值算子,提出了一種能夠與本文算法很好地結(jié)合的多重網(wǎng)格法。
In order to accelerate the convergence speed , we employ the local time step , and implicit residual smoothing methods . finally , we use this method to get the steady solution of the flow around naca0012 and naca4412 airfoil at very low speed and some basic unsteady solution 本文對(duì)在低馬赫數(shù)下繞naca0012翼型和naca4412翼型的定常流場(chǎng)進(jìn)行了求解,結(jié)果和實(shí)驗(yàn)基本吻合,并對(duì)非定常運(yùn)動(dòng)情況進(jìn)行了初步模擬研究,得出了一些有意義的結(jié)果。
4 . a 2 - d and 3 - d euler equations and n - s equations are solved using the cell - centered finite volume method and four - step runge - kutta scheme on the cartesian grids with standard convergence acceleration techniques such as local time stepping , enthalpy and implicit residual smoothing 使用jameson中心有限體積法和runge - kutta時(shí)間推進(jìn)方法,求解了關(guān)于二維、三維復(fù)雜流場(chǎng)的euler 、 navier - stokes方程,采用了當(dāng)?shù)貢r(shí)間步長(zhǎng)、隱式殘值光順等多種加速收斂方法。
The viscid flux is discretized by second - order central difference scheme . baldwin - lomax turbulence model is implemented in navier - stokes flow solver . for steady - state calculations , a four - stage runge - kutta scheme with convergence acceleration techniques such as local - time stepping and implicit residual smoothing is used 其中,定常計(jì)算中的時(shí)間推進(jìn)采用四步runge ? kutta方法,并應(yīng)用了當(dāng)?shù)貢r(shí)間步長(zhǎng)、隱式殘值光順等加速收斂措施;非定常計(jì)算中的時(shí)間推進(jìn)采用jameson的隱式雙時(shí)間方法。
The explicit method is widely used for its simpleness and little memory consumed with local time step and variable coefficients implicit residual smooth to accelerate the convergence procedure . according to yoon and jameson ' s ideas , an efficient implicit lu - sgs algorithm is carefully constructed by combing the advantages of lu factorization and symmetric - gauss - seidel technique in such a way to make use the l and u operators scalar diagonal matrices , thus the numeric algorithm requires only scalar inversion . the computational efficiency is greatly improved with this scheme 顯式方法具有簡(jiǎn)單,消耗內(nèi)存小等優(yōu)點(diǎn),并采用當(dāng)?shù)貢r(shí)間步長(zhǎng)、變系數(shù)隱式殘值光順等加速收斂措施,在定常流動(dòng)的模擬中得到了廣泛的應(yīng)用;根據(jù)yoon和jameson提出的簡(jiǎn)化正、負(fù)矩陣分裂,構(gòu)造的l 、 u算子只需進(jìn)行標(biāo)量對(duì)角陣求逆,極大提高了流場(chǎng)數(shù)值求解過程的計(jì)算效率;采用newton類型的偽時(shí)間子迭代技術(shù)使時(shí)間推進(jìn)精度提高至二階。
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(kù)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。
The cell - centered symmetric finite volume arithmetic and runge - kutta time stepping scheme are performed to solve euler equation . the two order and four order artificial dissipation is introduced for stability , local time stepping and implicit residual smoothing technique is applied to save computer time 在求解euler方程方面,采用格心格式的有限體積法進(jìn)行空間離散,四步runge - kutta法作時(shí)間推進(jìn),二階、四階人工耗散作為穩(wěn)定措施,還采用當(dāng)?shù)貢r(shí)間步長(zhǎng)和隱式殘值光順提高收斂速度。