發展求解NS與PNP耦合方程之方法

Abstract

本論文在有限差分的架構下發展一數值方法 以求解二維之對流-擴散方程。 首先發展兩個具有無條件單調性之五點離散格式， 再引入權重係數將兩離散格式做一線性之疊加， 使其具有色散關係保持的九點離散格式。 利用此一數值方法求解電液動(EHD)之非線性動力系統方程， 此系統包含了描述外加電場之Laplace方程、描述壁面所施加之電位分佈以及離子濃度分佈的Poisson-Nernst-Planck方程組及由庫倫力所驅動的不可壓縮Navier-Stokes方程組。 論文之內容主要是使用離子守恆Poisson-Nernst-Planck方程組，以描述電滲流模型，以觀察流速對離子分佈的影響， 以及描述受zeta電位所產生之電雙層，及描繪靠近壁面之速度邊界層、電荷擴散層等物理行為。

In this study the numerical scheme for solving the unsteady convection-diffusion scalar equation is developed in a domain of two dimensions. Two newly developed unconditionally monotonic five-point schemes, which have one common nodal point, are linearly combined through a weighting coefficient to yield the proposed nine-point conditionally monotonic scheme. Our main objective is to get a dispersively more accurate result from the nine-point stencil conditionally monotonic scheme. We also apply the nine-point stencil scheme to simulate Eelectroosmotic flow.The electroosmotic flow details in plannar and channels are revealed through this study with the emphasis placed an the formation of Coulomb force. The competition among the pressure gradient, diffusion and Coulomb forces leadings to the convective electroosmotic flow motion is also investigated in detail.