噴射式大氣電漿(APPJ)模擬研究---2D與3D平行化流體模型(II)

Abstract

在此研究計畫裡，我們計劃使用流體模式的技術，來模擬目前INER 所感興趣的噴 射式大氣電漿(APPJ)，或是更複雜的電漿狀態。並利用可彈性處理複雜的幾何形狀及平 行化的有限元素法(FEM)，來處理APPJ 離散化的偏微分方程式。 因為帶電粒子在鞘層區有很強的漂移效應(drift)，所以我們利用Stabilized-FEM 將其 連續方程離散化，而對於可在未來模擬各種流速或流體所需的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。而考慮到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 座標系統，以處理更真實的操作條件。所有的模擬程式將在PETSc 的AO 資料結構下 平行化。此後，程式可在任何平行化的機器上執行，例如: PC clusters。 總結來說，在這三年的計劃裡，我們第一年(01/01/2007-12/31/2007)的階段已開始進 行，並將這三年的研究方向及各階段工作做簡短敘述如下： 1st Year (01/01/2007-12/31/2007)：我們使用Stabilized FEM，已發展與正在驗證一套只考 慮帶電粒子的漂移-擴散近似與中性粒子的擴散傳輸，並已平行化的二維/軸對稱流體模 型程式。Stabilized FEM，是用以處理如鞘層區電漿參數變化較劇烈的地方，而對於複雜 的幾何結構，則使用三角或四角形網格處理較為適當。程式中的重要假設，包含了利用 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。同時也將使用Galerkin-FEM ，用以發展平行化的二維/軸對稱N-S equation solver。 2nd Year (01/01/2008-12/31/2008)：我們將持續發展及驗證N-S equation solver，並結合第 一年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，將使用Galerkin FEM 的N-S equation solver，修改為使用Stabilized-FEM 的N-S equation solve 後加以處 理。 3rd Year (01/01/2009-12/31/2009)：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 2-year project, which is the follow-on of the first year project that is undergoing now (01/01/2007-12/31/2007), we describe briefly what we are doing and will do it step by step as follows: 1st Year (01/01/2007-12/31/2007): We have developed and are currently verifying 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 or quadrilateral mesh is 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 (01/01/2008-12/31/2008): 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 (01/01/2009-12/31/2009): 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.