噴射式大氣電漿(APPJ)模擬研究---2D與3D平行化流體模型

Abstract

在此研究計畫裡，我們計劃使用流體模式模擬目前INER 感興趣的噴射式大氣電漿 (APPJ)或更複雜的電漿。我們使用適於處理複雜幾何與計算平行化的有限元素法(FEM) 離散求解APPJ 的物理方程式。 因 為 帶 電 粒子之連續方程在鞘層區有很強的漂移效應(drift) 所以我們利用 Stabilized-FEM 將其離散化，對於未來模擬各種流速流體所需的N-S equations 則以 Galerkin-FEM 或Stablized-FEM 離 散之。所有離散之耦合非線性方程式將利用 Newton-Krylov-Schwarz (NKS)方法進行數值解析。考慮到APPJ 的幾何結構,在第一階段 中我們首先發展一套程式用以模擬二維/軸對稱座標系統，之後將程式延伸至三維以處理 更真實的操作條件。所有的模擬程式將被平行化在PETSc 的AO 資料結構下。此後， 程式可在任何平行化的機器上執行，例如: PC clusters。 以下將就三年研究計畫各階段工作做簡短敘述: 1st Year:我們將使用Stabilized FEM 發展與驗證一套平行化的二維/軸對稱流體模型程 式，其中只考慮帶電粒子的漂移-擴散近似與中性粒子的擴散傳輸。Stabilized FEM 是用 以處理如鞘層區電漿參數變化較劇烈的地方，對於複雜的幾何結構使用三角形網格處理 較為適當。程式中重要假設包含利用drift-diffusion approximation 求解帶電粒子的動量通 量與使用local field approximation (LFA) 計算傳輸係數。同時， 我們也將使用 Galerkin-FEM 發展平行化的二維/軸對稱N-S equation solver。 2nd Year: 我們將持續發展與驗證N-S equation solver。之後，我們將結合第一年所發展 的流體模型程式與現階段已驗證的N-S code 以發展一套同時考慮中性粒子對流與擴散 傳輸的二維流體模型程式。至於大氣電漿中包含高速氣流的部份，我們則將使用Galerkin FEM 的N-S equation solver 修改為使用Stabilized-FEM 加以處理。 3rd Year: 我們將二維/軸對稱的流體模型程式延伸至三維以處理更真實的操作條件，同 時考慮帶電粒子的漂移-擴散近似與中性粒子的對流與擴散傳輸。對於複雜的幾何結構 則運用四面體網格加於處理。

In the proposed research project, we intend to apply the fluid modeling technique to simulate the atomospheric pressure plasma jet (APPJ), in which the INER is currently interested. We shall employ the finite element method (FEM) for all the PDEs involved in describing the APPJ since it is more flexible both in treating complicated geometry and parallel implementation. Stabilized FEM shall be used to discretize the continuity equation for all charged species considering the large drift term in the sheath, while Galerkin- or Stablized-FEM shall be used to discretize the N-S equations for possible all-speed flow simulation required in the future. All discretized nonlinear equations will be solved using a Newton-Krylov-Schwarz (NKS) scheme. Considering the flat or round APPJ, in which INER is interested, we will first develop a simulation code for 2D/axisymmetric coordinate system in the first phase and then extend it into a 3D version in later phases to deal with more realistic operating conditions. All simulation codes will be parallelized under the AO (Application Ordering) framework of PETSC. Eventually, they shall be able to run on any memory-distributed parallel machines, e.g., PC clusters. In summary, in this proposed 3-year project, we describe briefly how we will do it step by step as follows: 1st Year: We shall develop and verify a parallelized 2D/axisymmetric fluid modeling code using stabilized FEM, considering only diffusive neutral transport. Note stabilized FEM is used to treat plasma properties with large gradient, such as in the sheath. Triangular mesh will be used for easy adaptation to complicated geometry. Important assumptions include drift-diffusion approximation for the momentum fluxes of charges species and local field approximation (LFA) for evaluating transport coefficients. In addition, we shall also begin to develop a parallelized 2D/axisymmetric N-S equation solver using Galerkin FEM. 2nd Year: We shall continue the development and verification of parallelized 2D/axisymmetric N-S equation solver using Galerkin FEM. Later in this phase, we shall develop the fluid modeling code, which considers both the convective and diffusive transport for neutral species, by coupling the fluid modeling code developed in the 1st year and the verified N-S code earlier in this phase. In addition, we shall modify the N-S equation solver in the developed fluid modeling code from Galerkin- into Stabilized-FEM to treat plasma flows with higher speed. 3rd Year: We shall extend the 2D/axisymmetric fluid modeling code into a 3D fluid modeling code, considering both the convective and diffusive neutral transport. Tetrahedral mesh will be used for easy adaptation to complicated geometry.