Abstract of AMGBOUT Project

This proposal aims at extending the newly developed multigrid capabilities of BOUT++ in order to address new and relevant physics and allow for high performance simulations of 3D boundary plasma turbulence. BOUT++ is a flexible, modular framework to solve plasma physics relevant differential equations. It encompasses all necessary differential operators, boundary conditions and geometry. The CCFE version is used to study turbulence and motions of coherent structures in the edge of magnetic fusion machines. Such motion (and the transport related with it) depends on the electrostatic potential, which is determined by inverting a generalisation of the perpendicular Laplacian operator (represented by a second order linear elliptic PDE with non-constant coefficients). Previous work on the code, carried out with the help of the HLST, successfully introduced multigrid techniques to deal with this inversion but focused only on 2D solvers that independently calculate the potential on constant poloidal angle planes. Here, the derivatives along the parallel direction are neglected and the perpendicular Laplacian operator is incomplete. While this approximation is computationally convenient and often appropriate, it is however particularly ill-posed for strongly non-orthogonal coordinates, e.g. in the proximity of an X-point for field-aligned coordinates, where the parallel coordinate is almost tangential to the plane where the inversion is performed. The proposed work will use algebraic multigrid to extend the inversion to the parallel direction. This will allow efficient accurate reconstruction of the exact form of the Laplacian, and also allow solutions without making the Boussinesq approximation (when the Laplacian coefficients vary in the parallel direction). The resulting fully 3D solutions will lead to credible simulations in realistic tokamak geometry and will provide a more physically realistic solution for the electrostatic potential. This would pave the way for more extensive application of multigrid techniques to the inversions needed for implicit time stepping.