Theconvergence towards the weak solution is proved for one-dimensional space with initial and boundaryconditions by using some subtle techniques such as the estimate of spatial derivative, perturbationtheory and weak compactness 通過(guò)使用對(duì)空間導(dǎo)數(shù)的估計(jì)、弱緊性和奇異攝動(dòng)理論證明了有限元方法的收斂性。
Only clouds of points instead of grids are distributed over the computational domain and the spatial derivatives of the considered partial equations are estimated using a least-square curve fit on local clouds of points 與傳統(tǒng)的網(wǎng)格方法不同,無(wú)網(wǎng)格方法的核心是用“點(diǎn)云”離散求解區(qū)域,并基于當(dāng)?shù)攸c(diǎn)云離散結(jié)構(gòu),引入二次極小曲面逼近空間導(dǎo)數(shù)。
In the dissertation, the unstructured dynamic mesh technique is investigated . full implicit dual-time temporal derivatives and cell-center finite volume method spatial derivatives are adopted to simulate unsteady flow fields of 2-d airfoil, 3-d wing and wing-body configuration 在非結(jié)構(gòu)運(yùn)動(dòng)網(wǎng)格技術(shù)方面,本文發(fā)展了一種適用于解決非定常氣動(dòng)力計(jì)算的、高效的、魯棒性較好的非結(jié)構(gòu)運(yùn)動(dòng)網(wǎng)格方法。
Only clouds of points instead of grids are distributed over the computational domain and the spatial derivatives are estimated using a least-square curve fit on local clouds of points . the paper gives discrete form for euler equations on base of gridless method, and adopts five steps runge-kutta scheme for time-marching . the numerical results have been obtained for the 2-d flows over airfoils or multi-element airfoils using the method presented 本文首先對(duì)無(wú)粘euler方程進(jìn)行無(wú)網(wǎng)格離散,并運(yùn)用顯式runge-kutta格式推進(jìn)求解,成功地?cái)?shù)值模擬了二維單段和多段翼型的繞流;在此成功的基礎(chǔ)上通過(guò)在euler方程的右端加入粘性項(xiàng),使求解方程變?yōu)閷恿鱪avier?stokes方程,得到了翼型繞流,數(shù)值結(jié)果顯示出粘性的影響。