Transport and dynamcis in toroidal fusion systems. Final report, 1992--1995

This document is organized as follows. Discussions are presented on the properties of structured and unstructured meshes, and the data structures useful for describing them. Issues related to the triangulation of an arbitrary set of points in a plane are also discussed. A derivation is made of a finite volume approximation to the resistive MHD equations suitable for use on an unstructured, triangular mesh in toroidal geometry. Boundary conditions are discussed. The specific MHD model, and its implementation on the unstructured mesh, is discussed. A discussion is presented of methods of time integration, and descriptions are given for implementation of semi-implicit and fully implicit algorithms. Examples of the application of the method are given. Included are standard, two- dimensional hydrodynamic and MHD shock problems, as well as applications of the method to the equilibrium and stability of toroidal fusion plasmas in two and three dimensions. The initial results with mesh adaptation are also described