Warning

**PLEASE READ FIRST**

The results presented below are **preliminary** and for **my
personal use** only. My intent is to use these notes to communicate
with my close colleagues.

It is likely that the text of my notes **may undergo significant
revisions**. Although I have taken care, **many results might be
wrong**. That is just the nature of scientific work. If in doubt
please talk to me directly or send me an email to discuss.

If you are not a part of the Gkeyll project, please do not share or
use these results in any form whatsoever **without my explicit
permission**.

Note

Each note below also has links to the Lua script used to run the
simulation. Usually, the **links are in figure caption or in
tables**. They have (unhelpful at first) names like [*s5*]. If you want the exact initial
conditions, boundary conditions and other simulation details, please
click those links and look at the Lua script. The initial conditions
are in (obviously named) functions like init(). The script also
contains other details like exact setup (resolution, algorithms,
limiters, time-steps, etc). My goal is that others can reproduce
these results. Hence, there is no “hidden hand-of-god”, as one
commonly finds in some papers, etc.

Below are a list of journal entries, documenting various problems that have been attempted with Gkeyll. The eventual goal of Gkeyll is to solve the gyrokinetic equations in the edge region of tokamaks, including the scrap-off-layer. However, Gkeyll provides a powerful framework to study various physics problems as well as test different algorithms in a modular way. Some of these are documented below, with links to the Lua scripts to run those problems.

- The eigensystem of the Maxwell equations with extension to perfectly hyperbolic Maxwell equations
- The eigensystem of the Euler equations
- The MUSCL-Hancock scheme for solution of hyperbolic equations
- The eigensystem of the ten-moment equations
- Handling two-fluid five-moment and ten-moment source terms

- Simulation Index
- JE0: On reproducible research
- JE1: Solving Poisson equation on 2D periodic domain
- JE2: Benchmarking two finite-volume schemes for 1D Euler equations
- JE3: Testing the radiation transport equation solver in a homogeneous slab
- JE4: Two-fluid electromagnetic Riemann problems
- JE5: Hyperbolic balance laws with dispersive source terms
- JE6: Solving Maxwell equations with wave-propagation and FDTD schemes
- JE7: The dual Yee-cell FDTD scheme
- JE8: Propagation into a plasma wave beach
- JE9: Tunneling through an electron-cyclotron cutoff layer
- JE10: Ion-cyclotron wave (ICW) propagation and mode conversion
- JE11: Benchmarking a finite-element Poisson solver
- JE12: Studies with a discontinuous Galerkin Poisson bracket solver
- JE13: 2D Incompressible Euler Solver
- JE14: A DG scheme for Vlasov equation with fixed potential
- JE15: Studies with a DG electrostatic Vlasov solver
- JE16: Auxiliary equations and tests of local DG scheme for advection-diffusion equations
- JE17: Solving (Modified) Hasegawa-Wakatani equations
- JE18: Five-moment two-fluid reconnection on open domain
- JE19: On diffusion operators with discontinuous Galerkin schemes
- JE20: Vlasov equation on bounded domain
- JE21: Testing a solver for linearized electromagnetic GK equations
- JE22: Benchmarking dimensionally split finite-volume scheme for 2D Euler equations
- JE23: Benchmarking a finite-volume scheme for 3D Euler equations
- JE24: Tests for stair-stepped boundary Euler solver
- JE25: Three-wave models for Backward Raman and Brillouin Amplification
- JE26: Benchmarking a discontinuous Galerkin algorithm for Maxwell equations
- JE28: Some tests for Boltzmann-BGK equations
- JE29: Electrostatic shocks: kinetic and fluid
- JE30: Computing moments of a distribution function