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gyacomo/README.md
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HeLaZ (Hermite-Laguerre Z-pinch solver, 2020)
{img https://c4scdn.ch/file/data/fzljxlro5kbuv2wzw33h/PHID-FILE-zxq6uphjr3ziakuyjpxo/demo_phi_00.gif}
Roadmap : (Current version 1.4)
0. Write MOLI matlab solver in Fortran using Monli1D as starting point
0.0 go from 1D space to 2D fourier and from Hermite basis to Hermite-Laguerre basis
0.1 implement linear Poisson equation in fourier space
0.2 implement moment hierarchy linear terms
0.3 RK4 time solver
0.4 Benchmark with MOLI matlab results for Z-pinch (cf. kz_linear script)
Note : benchmark_*.m compares MOLI and HeLaZ linear results
0.5 Load COSOlver matrices
0.6 Benchmarks now include Dougherty, Lenard-Bernstein and Full Coulomb collision operators
Note : for full Coulomb, one must store a precomputed matrix from COSOlver in the iCa folder
1. Implementation of the non linear Poisson brackets term
1.0 FFTW3 has been used to treat the convolution as a product and discrete fourier transform
1.1 Methods in fourier_mod.f90 have been validated by tests on Hasegawa Wakatani system
1.1 Qualitative test : find similar turbulences as Hasegawa Wakatani system with few moments
1.2 Zonal flows are observed in a similar way to Ricci Rogers 2006 with GS2
1.3 Linear analysis showed that a certain amount of PJ are recquired to trigger mode
1.3.1 The \eta_B = 0.5 case is easier since it converged better in linear analysis than \eta_B = 1.0
1.3.2 Collisionality helps
1.4 Quantitative study with stationary average particle flux \Gamma_\infty
1.4.1 Convergence study of \Gamma_\infty w.r.t. P and J
1.4.2 Direct comparison with GS2 results of Ricci,Rogers 2006
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