計算火焰片模型的數值方法

Abstract

火焰片(flame sheet)模型的微分方程式是個非常非線性並且彼此互相相關的系統。在數值上為了解出這些方程式，我們使用了抑制牛頓法(damped Newton's method)並且結合單項網格法(one way multigrid)和Krylov子空間法(Krylov subspace methods)。 本篇論文的目的是研究對此模型下較有效率的Krylov子空間法，例如，雙共軛梯度穩定法(biconjugate gradient stabilized method)，廣義最小剩餘法(generalized minimum residual method) 和無轉置的擬最小剩餘法(transpose-free QMR method)。我們已經為此火焰片模型發展了C語言程式碼，並於文章內展示數值結果並且加以討論。

The differential equations of flame sheet model are highly nonlinear and strongly coupled system. To solve these equations numerically, we use damped Newton's method combining with one way multigrid method and Krylov subspace methods. The purpose of this thesis is to survey effective Krylov subspace methods for this model, for example, biconjugate gradient stabilized method (BICGSTAB), generalized minimum residual method (GMRES), and transpose-free QMR method (TFQMR). A code for the flame sheet model in C language is developed and numerical results will be presented and discussed in this work.