Development of a Vector Following Mesh Generator for Analysis of Two Dimensional Tokamak Plasma Transport

Abstract

A time-varying adaptive grid is required for multi-dimensional, time-dependent transport modeling of tokamak plasmas where the plasma equilibrium evolves according to plasma transport. In addition, a spatially inhomogeneous adaptive grid is needed for integrated transport modeling of different spatial scales. A number of mesh generators have been developed to provide calculation domains for two dimensional transport analyses mainly focused on the SOL-private region. However, generally these conventional mesh generators give a time-invariant grid without further updating during whole simulations. Therefore, these codes are unfavorable to simulate phenomena, where plasma properties vary significantly in time and space so that requiring continuous update of spatially inhomogeneous grids, appearing in the L-mode to H-mode transition, Edge Localized Modes (ELMs), and so on. A new adaptive mesh generator is developed in this thesis for 2-D core-edge coupled transport simulations specified for plasma conditions where the plasma configuration is rather fixed but internal equilibrium is still dynamically varying. The geometric mesh type of the field aligned orthogonal structured mesh is employed appropriate for the Finite Volume Method (FVM) which decomposes the parallel and the radial direction to the magnetic field due to strong anisotropy of transport in a magnetized plasma. Thus, the mesh is created orthogonally based on the poloidal magnetic field map of given boundary equilibrium profiles suitable for both Single Null (SN) and Double Null (DN) divertor configurations. It is also developed to attain flexibility in generating grid distributions for optimizing calculation domains according to various plasma phenomena which one focuses in transport modeling. The mesh generator can generate spatially non-uniform grids by considering different spatial scales when treating global and highly localized phenomena simultaneously. In general, because there is no transformation relation between the plasma transport equation and the discretization equation, the mesh generation is operated by algebraic assumptions like an interpolation scheme. In this condition, the vector following method is introduced to find a desired position by using information of the poloidal magnetic field map. The newly developed mesh generator is evaluated in three way. Firstly, it is applied to produce a mesh for a KSTAR geometry where the plasma equilibrium is taken from the Tokamak Equilibrium Solver (TES) code. The property of the generated mesh is evaluated in a quantitative way by introducing some mesh quality factors based on a criterion of the flux conservation in the FVM method. Secondly, the mesh generator is verified with a conventional code, CARRE in terms of the mesh quality factors. It is found that the numerical results are generally similar between them but an improvement in the private region is detected in the newly developed code near the divertor region. Furthermore, the radial flux error at the separatrix lines is more alleviated than the CARRE code, which is more desirable to simulate plasma boundary physics such as Multifaceted Asymmetric Radiation From the Edge (MARFE) and ELMs. Thirdly, the capability of the non-uniform grid generation is evaluated. Non-uniform grids are produced in the core region in two ways. One is generated by considering the ion Larmor radius and the other by considering local steep gradients such as transport barriers. They are compared with a reference case with uniform distribution. A more refined grid is found near the edge region characterized with smaller ion Larmor radius and steeper gradient whereas coarser one in the core. Such fine grid at the edge region is indeed suitable for analysis of edge-SOL transport. The developed vector following mesh generator in this thesis will deal with adaptable meshes changing with time according to the equilibrium evolution by directly connected with the transport solver for coupled time-dependent core-edge SOL simulations.