【摘要】：湍流輸運(yùn)是磁約束等離子體研究的重要課題之一。準(zhǔn)線性理論很好地預(yù)言了一些情況下系統(tǒng)的輸運(yùn)。然而在更多的非線性情況下,由湍流導(dǎo)致的系統(tǒng)輸運(yùn),在理論上仍然很難處理。隨著計(jì)算機(jī)技術(shù)的發(fā)展,數(shù)值模擬已經(jīng)在等離子體湍流輸運(yùn)研究中扮演著越來越重要的角色。本文首先介紹了基于全新的數(shù)值李變換方法所開發(fā)一維無碰撞Vlasov系統(tǒng)的模擬程序。新的程序以I-變換理論為基礎(chǔ),數(shù)值上結(jié)合了連續(xù)性方法以及特征線方法,即避免了粒子模擬存在較大系統(tǒng)噪聲的問題,又兼具了特征線方法較強(qiáng)的數(shù)值穩(wěn)定性的特點(diǎn),在模擬中能采用比較長(zhǎng)的時(shí)間步長(zhǎng)。計(jì)算中,我們利用多步變換的方法,在數(shù)值上完美地解決了微擾方法在粒子俘獲問題上固有的困難,使得程序能夠準(zhǔn)確地模擬系統(tǒng)線性階段以及非線性階段的演化。在一維Landau阻尼問題以及雙峰不穩(wěn)定性問題的算例中,新程序的計(jì)算結(jié)果與傳統(tǒng)方法得到的結(jié)果一致。然后我們利用新程序分析了隨機(jī)電場(chǎng)擾動(dòng)問題以及雙峰不穩(wěn)定性問題中粒子在速度空間的輸運(yùn)。相較于傳統(tǒng)的模擬方法,新的基于微擾理論的模擬方法其中間變量與輸運(yùn)系數(shù)有著直接的關(guān)聯(lián),在數(shù)值計(jì)算中能夠方便地得到系統(tǒng)的輸運(yùn)系數(shù)。模擬的結(jié)果顯示,在系統(tǒng)受到隨機(jī)場(chǎng)擾動(dòng)和線性階段的湍流擾動(dòng)時(shí),利用新的模擬方法得到的輸運(yùn)系數(shù)與實(shí)際的結(jié)果吻合。而在湍流的非線性階段,由于大尺度結(jié)構(gòu)的存在,新方法以及準(zhǔn)線性方法所計(jì)算得到的輸運(yùn)系數(shù)與實(shí)際的結(jié)果有了較大的偏差。接著我們利用數(shù)值李變換程序計(jì)算了一維無碰撞系統(tǒng)演化過程中的熵產(chǎn)生。與傳統(tǒng)數(shù)值上用于計(jì)算熵的公式不同,我們采用了理論上廣為接受的利用粗網(wǎng)平均分布函數(shù)來計(jì)算系統(tǒng)熵產(chǎn)生的方法。在隨機(jī)擾動(dòng)場(chǎng)算例,線性Landau阻尼算例和雙峰不穩(wěn)定性算例中,我們發(fā)現(xiàn)隨著粗網(wǎng)平均長(zhǎng)度的增加,計(jì)算所得的熵產(chǎn)生是收斂的,并且當(dāng)分布函數(shù)與麥克斯韋分布接近時(shí),我們計(jì)算所得到的熵產(chǎn)生,與熱力學(xué)定義的熵產(chǎn)生是一致的。我們還討論了上述情況中粗網(wǎng)平均長(zhǎng)度的選取對(duì)計(jì)算所得熵產(chǎn)生的影響以及非麥克斯韋分布對(duì)熵計(jì)算的影響。最后,討論了基于數(shù)值李變換方法發(fā)展的環(huán)位形非線性回旋動(dòng)理學(xué)模擬程序NLT非線性調(diào)試中的守恒性問題和濾波問題的處理方法。
[Abstract]:Turbulent transport is one of the most important topics in the study of magnetically confined plasma. The quasilinear theory well predicts the transport of the system in some cases. However, in more nonlinear cases, the system transport caused by turbulence is still difficult to deal with theoretically. With the development of computer technology, numerical simulation has played a more and more important role in the study of plasma turbulence transport. This paper first introduces the simulation program of one-dimensional collision-free Vlasov system based on the new numerical lie transform method. The new program is based on the I- transformation theory and combines the continuity method and the feature line method numerically, which avoids the problem of large system noise in particle simulation and has the characteristics of strong numerical stability of the feature line method. A longer time step can be used in the simulation. In the computation, we use the multi-step transformation method to solve the inherent difficulty of the perturbation method in the particle capture problem numerically, so that the program can accurately simulate the evolution of the linear and nonlinear stages of the system. In the case of one-dimensional Landau damping problem and bimodal instability problem, the results obtained by the new program are in agreement with those obtained by the traditional method. Then we use the new program to analyze the particle transport in the velocity space in the stochastic electric field perturbation problem and the bimodal instability problem. Compared with the traditional simulation method, the new simulation method based on perturbation theory has a direct correlation between the intermediate variables and the transport coefficient, and the transport coefficient of the system can be easily obtained in the numerical calculation. The simulation results show that the transport coefficients obtained by the new simulation method are in good agreement with the actual results when the system is subjected to random field disturbances and linear turbulence disturbances. However, in the nonlinear stage of turbulence, due to the existence of large-scale structures, the transport coefficients calculated by the new method and the quasi-linear method are quite different from the actual results. Then we use the numerical lie transform program to calculate the entropy generation in the evolution of one dimensional collision-free systems. Different from the traditional formula used to calculate entropy, we adopt the widely accepted method of calculating the entropy of the system by using the mean distribution function of rough net. In the examples of random disturbance field, linear Landau damping and bimodal instability, we find that the entropy generation is convergent with the increase of average length of rough net, and when the distribution function is close to Maxwell distribution, The entropy generated by our calculations is consistent with the entropy generation defined by thermodynamics. We also discuss the influence of the average length of the rough net on the calculated entropy and the influence of the non-Maxwell distribution on the entropy calculation. Finally, the conservation and filtering problems in NLT nonlinear cyclotron simulation program based on the numerical lie transform method are discussed.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O53

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