發(fā)布時(shí)間：2018-01-23 12:37

  本文關(guān)鍵詞： S_N 輸運(yùn)方程 多群輻射擴(kuò)散方程 離散縱標(biāo)方法 簡單隅角平衡方 法 h自適應(yīng) 扭曲網(wǎng)格 耦合建模 區(qū)域分解 并行離散格式　出處：《中國工程物理研究院》2016年博士論文　論文類型：學(xué)位論文

【摘要】：輸運(yùn)問題在慣性約束聚變和武器物理等領(lǐng)域中有著廣泛而重要的應(yīng)用,它具有多變量、多尺度、多物理等特征,其數(shù)值模擬難度居現(xiàn)代科學(xué)計(jì)算領(lǐng)域的前列。實(shí)際應(yīng)用中輸運(yùn)方程的求解存在如下的問題：1)數(shù)值解出現(xiàn)非物理振蕩、出負(fù)等現(xiàn)象；2)大變形網(wǎng)格下的計(jì)算精度較低,有時(shí)甚至計(jì)算失敗；3)數(shù)值計(jì)算代價(jià)昂貴。本文主要針對上述問題,為提高輸運(yùn)方法的健壯性開展相關(guān)的離散格式和自適應(yīng)算法研究,并為了提高求解效率開展多物理耦合模擬及并行算法研究,為實(shí)際應(yīng)用問題提供算法與技術(shù)支撐。本文主要成果如下：(1)對一維粒子輸運(yùn)方程的子網(wǎng)格平衡格式開展了理論研究,證明了該格式的穩(wěn)定性和收斂性；并通過分析格式設(shè)計(jì)的不足,提出了基于嵌套網(wǎng)格的兩種離散格式。數(shù)值結(jié)果表明,新格式的精度要優(yōu)于步格式,與菱形格式、子網(wǎng)格平衡格式的精度相當(dāng),且能明顯抑制菱形格式和子網(wǎng)格平衡格式計(jì)算中的非物理振蕩。對于強(qiáng)散射問題的計(jì)算,新格式的迭代收斂速度較快。(2)對耦合流體計(jì)算的二維輻射傳輸問題中存在的因網(wǎng)格大變形導(dǎo)致精度較低及掃描死鎖問題,提出了一種采用三角剖分的改進(jìn)子網(wǎng)格平衡格式,并設(shè)計(jì)了基于網(wǎng)格幾何品質(zhì)的h自適應(yīng)加密輸運(yùn)算法,與原有算法相比,新算法能改善大變形網(wǎng)格上的計(jì)算精度,并且解決了實(shí)際應(yīng)用問題中由于凹網(wǎng)格死鎖帶來的“算不下去”的問題。進(jìn)一步,在間斷有限元的框架下給出了混雜網(wǎng)格上輸運(yùn)算法的穩(wěn)定性和收斂性證明。(3)對輸運(yùn)問題的不同層次建模,開展了多群擴(kuò)散與單群擴(kuò)散、多群擴(kuò)散與單溫?zé)醾鲗?dǎo)兩種耦合建模的數(shù)值模擬方法研究.基于區(qū)域分解的方法求解耦合模型,并分別提出了自洽的耦合界面連接條件,數(shù)值模擬結(jié)果表明,耦合建模計(jì)算精度與單一精細(xì)建模的計(jì)算精度相當(dāng),其計(jì)算代價(jià)與低層次建模的計(jì)算代價(jià)相當(dāng)。(4)對二維擴(kuò)散方程提出了一種無條件穩(wěn)定的具有二階精度的單元中心型守恒并行離散格式,格式的構(gòu)造不需要預(yù)估和校正步,并且滿足離散的能量守恒。理論上嚴(yán)格證明了離散數(shù)值解在H1范數(shù)下的無條件穩(wěn)定性和二階收斂性,數(shù)值實(shí)驗(yàn)驗(yàn)證了理論分析的結(jié)果。
[Abstract]:Transport problem has been widely used in inertial confinement fusion and weapon physics. It has the characteristics of multi-variable, multi-scale, multi-physics and so on. The difficulty of numerical simulation is in the forefront of modern scientific calculation. In practical application, there exists the following problems in solving the transport equation: 1) the numerical solution has the phenomena of non-physical oscillation and negative. 2) the calculation accuracy of large deformation mesh is low, and sometimes it even fails; 3) numerical computation is expensive. In this paper, the discrete scheme and adaptive algorithm are studied in order to improve the robustness of transport methods. And in order to improve the efficiency of solving the multi-physical coupling simulation and parallel algorithm research. The main results of this paper are as follows: (1) the subgrid equilibrium scheme of one-dimensional particle transport equation is studied theoretically, and the stability and convergence of the scheme are proved. Two discrete schemes based on nested meshes are proposed by analyzing the shortcomings of the scheme design. The numerical results show that the accuracy of the new scheme is better than that of the step scheme and the precision of the subgrid balance scheme is the same as that of the rhombus scheme. Moreover, the non-physical oscillation in the calculation of rhombus scheme and sub-grid balance scheme can be obviously suppressed, and the strong scattering problem can be calculated. The iterative convergence rate of the new scheme is faster. (2) in the two-dimensional radiative transmission problem of coupled fluid computation, the problem of low precision and scanning deadlock caused by large mesh deformation exists. An improved submesh balance scheme using triangulation is proposed, and an h adaptive encryption transport algorithm based on mesh geometry quality is designed, which is compared with the original algorithm. The new algorithm can improve the computational accuracy on large deformed meshes, and solve the problem of "not being able to calculate" caused by the deadlock of concave meshes in practical applications. In the framework of discontinuous finite element, the stability and convergence proof of the transport algorithm on hybrid meshes is given, and the multi-group diffusion and single-group diffusion are developed. The numerical simulation method of multi-group diffusion and single-temperature heat conduction coupling modeling is studied. The domain decomposition method is used to solve the coupled model and the self-consistent coupling interface connection conditions are proposed respectively. The numerical simulation results show that. The computational accuracy of coupled modeling is equivalent to that of single fine modeling. The computational cost is the same as that of low level modeling.) an unconditionally stable conserved conserved parallel discrete scheme with second-order accuracy is proposed for two-dimensional diffusion equations. The construction of the scheme does not require the prediction and correction steps, and satisfies the discrete energy conservation. In theory, the unconditional stability and the second order convergence of the discrete numerical solutions under the H 1 norm are strictly proved. The results of theoretical analysis are verified by numerical experiments.
【學(xué)位授予單位】：中國工程物理研究院
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O241.82

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