本文選題：經(jīng)典相對論歐拉方程組 + 等熵相對論歐拉方程組��； 參考：《云南大學》2016年博士論文

【摘要】：本文研究兩類相對論流體力學方程組的流擾動問題.第一類是描述動量守恒和能量守恒的經(jīng)典相對論歐拉方程組,第二類是描述重子數(shù)守恒和動量守恒的等熵相對論歐拉方程組.首先,通過求解帶有流擾動的零壓相對論歐拉方程組的黎曼問題,發(fā)現(xiàn)了兩類有趣的U-型擬真空狀態(tài)解和參數(shù)化的狄拉克激波解.進而證明,當流擾動消失時,參數(shù)化的狄拉克激波和U-型擬真空狀態(tài)解收斂到零壓相對論歐拉方程組的狄拉克激波和真空狀態(tài)解.其次,在不同的氣體狀態(tài)方程下,使用特征線分析法和相平面分析法,借助于洛倫茲變換,依次構造性地求解了相應系統(tǒng)的黎曼問題.進一步地,嚴格證明了,當壓力或者流擾動消失時,相對論歐拉方程組的黎曼解收斂到它對應的零壓流系統(tǒng)的狄拉克激波和真空解.這表明,零壓相對論歐拉方程組的狄拉克激波和真空解對于流擾動是穩(wěn)定的.第一章介紹相對論流體力學方程組的研究現(xiàn)狀和本文的研究工作.第二章討論基于經(jīng)典相對論歐拉方程組的零壓相對論歐拉方程組的黎曼問題,構造了狄拉克激波解和真空解.第三章考慮經(jīng)典相對論歐拉方程組的流擾動問題.首先,求解一類純流擾動的零壓相對論歐拉方程組的黎曼問題,獲得了倒U-型的擬真空狀態(tài)解和參數(shù)化的狄拉克激波解.隨后證明,當流擾動消失時,參數(shù)化的狄拉克激波解和倒U-型的擬真空狀態(tài)解分別收斂到零壓相對論歐拉方程組的狄拉克激波解和真空解.其次,求解經(jīng)典相對論歐拉方程組在包含壓力的流擾動下的黎曼問題.當雙參數(shù)的流擾動消失時,我們嚴格證明了,包含兩個激波的黎曼解趨于零壓相對論歐拉方程組的狄拉克激波解；包含兩個疏散波的黎曼解趨于零壓相對論歐拉方程組的兩個接觸間斷解,并且介于這兩個激波之間的非真空狀態(tài)趨于真空.第四章研究經(jīng)典相對論修正Chaplygin氣體方程組在壓力和流擾動分別消失時,黎曼解的極限行為.我們首先求解該系統(tǒng)的黎曼問題,并分析基本波曲線對參數(shù)的依賴性.隨后證明,當雙參數(shù)的壓力擾動和三參數(shù)的流擾動分別消失時,包含兩個激波的黎曼解收斂到零壓相對論歐拉方程組的狄拉克激波解；包含兩個疏散波以及一個非真空中間狀態(tài)的黎曼解收斂到零壓相對論歐拉方程組的真空解.第五章求解基于等熵相對論歐拉方程組的零壓相對論歐拉方程組的狄拉克激波和真空狀態(tài).第六章研究帶有流擾動的等熵相對論歐拉方程組.首先求解一類特殊的純流擾動的零壓相對論歐拉方程組的黎曼問題,構造了U-型的擬真空狀態(tài)解和參數(shù)化的狄拉克激波解.進而證明,當流擾動消失時,U-型的擬真空狀態(tài)解和參數(shù)化的狄拉克激波解分別收斂到對應的零壓相對論歐拉方程組的狄拉克激波解和真空解.其次,求解具有流擾動的等熵相對論多方氣體歐拉方程組的黎曼問題.進一步地,我們嚴格證明,當壓力和雙參數(shù)的流擾動消失時,包含兩個激波的黎曼解收斂到對應的零壓流系統(tǒng)的狄拉克激波解,并且介于這兩個激波之間的中間密度趨于一個加權的狄拉克δ-測度即形成狄拉克激波；而包含兩個疏散波的黎曼解收斂到零壓相對論歐拉方程組的接觸間斷解,并且它們之間的非真空狀態(tài)趨于真空.第七章考慮等熵相對論修正Chaplygin氣體歐拉方程組的流擾動問題.首先.求解系統(tǒng)的黎曼問題,并構造黎曼解.其次,我們證明,當雙參數(shù)壓力和三參數(shù)流擾動分別消失時,包含兩個激波的黎曼解趨于相應的零壓相對論歐拉方程組的狄拉克激波解；包含兩個疏散波的黎曼解趨于零壓相對論歐拉方程組的接觸間斷解,并且介于這兩個疏散波之間的非真空狀態(tài)趨于真空.
[Abstract]:In this paper, we study the flow disturbance of two kinds of relativistic fluid mechanics equations. The first class is the classical relativistic Euler equation describing the conservation of momentum and the conservation of energy. The second is the isentropic relativistic Euler equation describing the conservation of baryon number and the conservation of momentum. First, the zero pressure relativistic Euler equations with flow disturbance are solved. In Riemann's problem, two kinds of interesting U- quasi vacuum state solutions and parameterized Dirac shock wave solutions are found. Further, it is proved that when the flow disturbance disappears, the parameterized Dirac shock and U- quasi vacuum state solutions converge to the zero pressure relativistic Euler equation group of Dirac shock and vacuum state. Second, under different gas state equations, Using the method of characteristic line analysis and phase plane analysis, the Riemann problem of the corresponding system is solved by means of Lorenz transform. Further, it is proved strictly that when the pressure or flow disturbance disappears, the Riemann solution of the relativistic Euler equation converges to the Dirac shock and the vacuum solution of its corresponding zero pressure flow system. The Dirac shock wave and the vacuum solution of the Euler equation in the relativistic system of zero pressure are stable. The first chapter introduces the research status of the relativistic fluid mechanics equations and the research work in this paper. The second chapter discusses the Riemann problem of the zero pressure relativistic Euler equation based on the classical relativistic Euler equation, and constructs the Dirac excitation. In the third chapter, the third chapter considers the flow perturbation problem of the classical relativistic Euler equations. First, the Riemann problem of a class of zero pressure relativistic Eulerian equations of a class of pure flow perturbation is solved. The pseudo vacuum state solution of the inverted U- and the parameterized Dirac shock solution are obtained. Then, it is proved that the parameterized Dirac shock wave when the flow disturbance disappears. The quasi vacuum state solution of the solution and inverted U- converges to the Dirac shock solution and the vacuum solution of the zero pressure relativistic Euler equation group. Secondly, we solve the Riemann problem of the classical relativistic Euler equation under the flow disturbance containing pressure. When the two parameter flow disturbance disappears, we strictly prove that the Riemann solution containing two shock waves tends to zero. The Dirac shock wave solution of the pressure relativistic Euler equation; the Riemann solution containing two evacuation waves tends to two contact discontinuous solutions to the zero pressure relativistic Euler equation, and the non vacuum state between the two shock waves tends to vacuum. The fourth chapter studies the classical relativistic modified Chaplygin gas equations in pressure and flow perturbation respectively. We first solved the Riemann problem of the Riemann solution and analyzed the dependence of the basic wave curve on the parameters. Then, it was proved that when the two parameter pressure disturbance and the three parameter flow disturbance disappeared, the Riemann solution containing two shock waves converged to the Dirac shock solution of the zero pressure relativistic Euler equation; The Riemann solution containing two evacuation waves and a non vacuum intermediate state converges to the vacuum solution of the zero pressure relativistic Euler equation. The fifth chapter solves the Dirac shock and vacuum state of the Euler equation group based on the isentropic relativistic Euler equation. The sixth chapter studies the isentropic relativistic Euler equations with the flow disturbance. First, the Riemann problem of a class of zero pressure relativistic Euler equations of a special kind of pure flow is solved. The quasi vacuum state solution of U- type and the parameterized Dirac shock wave solution are constructed. Then, it is proved that when the flow disturbance disappears, the quasi vacuum state solution of the U- type and the parameterized Dirac shock solution converge to the corresponding zero pressure relativistic Euler square, respectively. The Dirac shock wave solution and the vacuum solution in the process group. Secondly, to solve the Riemann problem of the isentropic Euler equation with the isentropic relativistic gas. Further, we prove that when the pressure and the two parameter flow disturbance disappear, the Riemann solution containing two shock waves converges to the Dirac shock wave solution for the zero pressure flow system. The middle density between the two shock waves tends to a weighted Dirac delta measure to form a Dirac shock wave, and the Riemann solution containing two evacuation waves converges to the contact discontinuous solution of the zero pressure relativistic Euler equation, and the non vacuum state between them tends to vacuum. The seventh chapter considers the isentropic relativity to amend the Chaplygin gas. The Riemann problem of the Euler equation is solved. First, the Riemann problem is solved and the Riemann solution is constructed. Secondly, we prove that when the two parameter pressure and the three parameter flow disturbance disappear respectively, the Riemann solution containing two shock waves tends to the corresponding zero pressure relativistic Eulerian equation of the Dirac shock wave, and the Riemann solution containing two evacuation waves. In the zero pressure relativistic Euler equations, the contact discontinuity solution and the non vacuum state between these two scattered waves tend to vacuum.

【學位授予單位】：云南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O35

【相似文獻】

相關期刊論文 前10條

1 何啟發(fā),劉定勝;歐拉方程的算子算法[J];湖北民族學院學報(自然科學版);2000年04期

2 宋澤成;;關于歐拉方程的進一步討論[J];唐山師范學院學報;2010年02期

3 廖為鯤;;淺談歐拉方程的計算[J];科技視界;2013年20期

4 劉友瓊;任炯;梁楠;;一種求解歐拉方程的新的矢通量分裂方法[J];紡織高校基礎科學學報;2013年03期

5 胡勁松;關于二階歐拉方程的求解[J];四川師范大學學報(自然科學版);2003年06期

6 李岳生;;分布歐拉方程與分片函數(shù)的表示[J];計算數(shù)學;2006年03期

7 高夫征;求解歐拉方程組的一類新型自適應多分辨格式[J];山東大學學報(工學版);2003年06期

8 高真圣;張培欣;;二維等熵可壓歐拉方程古典解的存在性(英文)[J];數(shù)學研究;2013年03期

9 嚴家良;;兩類歐拉方程的特解表達式[J];廣東民族學院學報(自然科學版);1989年04期

10 胡勁松;齊次歐拉方程的另一種求解方法[J];重慶工學院學報;2004年01期

相關會議論文 前1條

1 趙桂萍;許為厚;任鍵;;統(tǒng)一坐標法求解二維歐拉方程[A];第十屆全國激波與激波管學術討論會論文集[C];2002年

相關博士學位論文 前1條

1 張宇;相對論歐拉方程組的流擾動問題[D];云南大學;2016年

相關碩士學位論文 前7條

1 段暢通;等熵相對論歐拉方程組的周期解[D];上海交通大學;2009年

2 于戰(zhàn)華;跨聲速歐拉方程并行算法研究及應用[D];南京航空航天大學;2004年

3 隋玉霞;二維可壓歐拉方程組徑向?qū)ΨQ解的爆破[D];南京大學;2014年

4 靳鯤鵬;二維Quasi-Geostrophic方程的幾何約束與非爆炸性[D];復旦大學;2008年

5 韋祥文;MPI平臺下二維歐拉方程數(shù)值解法[D];西北工業(yè)大學;2003年

6 齊進;歐拉方程Roe格式與高精度半拉氏方法研究[D];中國工程物理研究院;2010年

7 龔凱;有限翼展撲動翼的歐拉方程數(shù)值模擬[D];西北工業(yè)大學;2003年

，

本文編號：1779213