陳宜良臺灣大學：數學研究所劉音宏Liu, Yin-HungYin-HungLiu2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59421在這篇論文中, 我們用氣體動力學的方法, 探討守恆律方程的問題。 其中針對非凸性流量的情形, 設計在氣體平衡時拋物線型的速率分布函數。In this paper, we use the concept of gas-kinetic schemes to solve the equations of conservation laws. For non-convex fluxes, we can construct the parabolic distribution function for the equilibrium state.Contents 中文摘要 ii Abstract iii 1 Probability Density Distribution Function 1 1.1 Maxwell-Boltzmann Distribution . . . . . . . . . . . . . . . . 1 1.2 Parabolic Distribution . . . . . . . . . . . . . . . . . . . . . . 2 2 Kinetic Flux Vector Splitting Scheme 4 2.1 First Order KFVS . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Second Order KFVS . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Stability Analysis For The KFVS For The Linear Advection Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 The Modified Equation For Linear Advection Equation . . . . 6 3 KFVS For Scalar Conservation LawsWith Non-Convex Fluxes 9 3.1 Non-Convex Flux Equation . . . . . . . . . . . . . . . . . . . 9 3.2 Less Dissipative Scheme . . . . . . . . . . . . . . . . . . . . . 10 3.3 The Modified Equation For Non-Convex Flux Equation . . . . 12 3.4 2 × 2 System of The Elastic-Plastic Model . . . . . . . . . . . 15 3.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.6 Conclution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 A Moments of distribution function 18 A.1 Maxwellian Distribution Function . . . . . . . . . . . . . . . . 18 A.2 Parabolic Distribution Function . . . . . . . . . . . . . . . . . 19 B Examples 20568186 bytesapplication/pdfen-US氣體動力學守恆律方程非凸性gas-kineticconservation lawnon-convexthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59421/1/ntu-96-R94221040-1.pdf