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An overview of the algorithm and a sampling of plasma applications of the implicit, adaptive high order finite (spectral) element modeling framework, HiFi, is presented. The distinguishing capabilities of the HiFi code include adaptive spectral element spatial representation with flexible geometry, highly parallelizable implicit time advance, and general flux-source form of the partial differential equations and boundary conditions that can be implemented in its framework. Early algorithm development and extensive verification studies of the two-dimensional version of the code, known as SEL, have been previously described [A.H. Glasser & X.Z. Tang, Comp. Phys. Comm., 164 (2004); V.S. Lukin, Ph.D. thesis, Princeton University (2008)]. Here, substantial algorithmic improvements and extensions are presented together with examples of two- and three- dimensional applications of the HiFi framework. These include a Cartesian two-dimensional incompressible magnetohydrodynamic simulation of low dissipation magnetic reconnection in a large system, a two-dimensional axisymmetric simulation of self-similar compression of a magnetic plasma confinement configuration, and a three-dimensional Hall MHD simulation of spheromak tilting and relaxation. Some planned efforts to further improve and expand the capabilities of the HiFi modeling framework are discussed.
A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak X-point geometry, the code is able to simulate a wide range of fluid mod
We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys. Plasmas 18, 102309
The document describes a numerical algorithm to simulate plasmas and fluids in the 3 dimensional space by the Euler method, in which the spatial meshes are fixed to the space. The plasmas and fluids move through the spacial Euler mesh boundary. The E
Here we present details of a mixed implicit-explicit numerical scheme for the solution of the gyrokinetic-Poisson system of equations in the local limit. This scheme has been implemented in a new code called $texttt{stella}$, which is capable of evol
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigri