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https://github.com/cchandre/vm15d

Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations
https://github.com/cchandre/vm15d

fluid-simulation fluid-solver hamiltonian kinetic-modeling mathematica matlab numpy plasma-physics python3 scipy vlasov-equation vlasov-solver

Last synced: 2 days ago
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Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations

Host: GitHub
URL: https://github.com/cchandre/vm15d
Owner: cchandre
License: bsd-2-clause
Created: 2021-04-29T16:03:23.000Z (over 3 years ago)
Default Branch: main
Last Pushed: 2022-09-27T16:03:06.000Z (over 2 years ago)
Last Synced: 2024-11-10T21:11:46.382Z (2 months ago)
Topics: fluid-simulation, fluid-solver, hamiltonian, kinetic-modeling, mathematica, matlab, numpy, plasma-physics, python3, scipy, vlasov-equation, vlasov-solver
Language: Mathematica
Homepage:
Size: 2.12 MB
Stars: 1
Watchers: 1
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

README

        # VM15D : Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations

- **VM15D.nb**: [Mathematica notebook] checks the Jacobi identity and the Casimir invariants for the bracket Bracket[F,G] given by Eq. (6) of the article  *Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations* by C. Chandre and B.A. Shadwick

- **GrowthRates.mlx**: [Matlab livescript] computes the growth rates for the linearized equations of motion near a homogeneous equilibrium. It reproduces the figures of the article *Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations* by C. Chandre and B.A. Shadwick

- `VM15D python code`

  - [`VM15D_dict.py`](https://github.com/cchandre/VM15D/blob/main/VM15D_dict.py): to be edited to change the parameters of the VM15D computation (see below for a dictionary of parameters)

  - [`VM15D.py`](https://github.com/cchandre/VM15D/blob/main/VM15D.py): contains the VM15D class and main functions (not to be edited)

  - [`VM15D_modules.py`](https://github.com/cchandre/VM15D/blob/main/VM15D_modules.py): contains the methods to run VM15D (not to be edited)

  - Once [`VM15D_dict.py`](https://github.com/cchandre/VM15D/blob/main/VM15D_dict.py) has been edited with the relevant parameters, run the file as 

  ```sh

  python3 VM15D.py

  ```

  - NB: in case of error, check your version of the python modules used in the code (see [`modules_version.txt`](https://github.com/cchandre/VM15DD/blob/main/modules_version.txt))

___

##  Parameter dictionary for VM15D

- *Tf*: double; duration of the integration (in units of *ω_p^-1*)

- *alpha*: double; value of the parameter *α* of the closure

- *lam*: double; value of the parameter *λ* of the closure

- *integrator_kinetic*: string ('position-Verlet'); choice of solver for the integration of the Vlasov equation

- *nsteps*: integer; number of steps in one period of plasma oscillations (1/*ω_p^{*) for the integration of the Vlasov equation

- *integrator_fluid*: string ('RK45', ‘RK23’, ‘DOP853’, ‘BDF’, ‘LSODA’); choice of solver for the integration of the fluid equation

- *precision*: double; numerical precision of the integrator for the fluid equations; threshold for the Fourier transforms

- *n_casimirs*: integer; number of Casimir invariants to be monitored}

- *Lz*: double; the *z*-axis is (-*Lz*, *Lz*)

- *Lvx*: double; the *vx*-axis is (-*Lvx*, *Lvx*)

- *Lvz*: double; the *vz*-axis is (-*Lvz*, *Lvz*)

- *Nz*: integer; number of points in *z* to represent the field variables

- *Nvx*: integer; number of points in *vx* to represent the field variables

- *Nvz*: integer; number of points in *vz* to represent the field variables

- *f_init*: lambda function; initial distribution *f*(*z*,*vx*,*vz*,*t*=0)

- *Kinetic*: list of strings in ['Compute', 'Plot']; list of instructions for the 1.5D Vlasov-Maxwell simulation

- *Fluid*: list of strings in ['Compute', 'Plot']; list of instructions for the fluid simulation; if contains 'Save', the results are saved in a `.mat` file

- *darkmode*: boolean; if True, plots are done in dark mode

- *tqdm_display*: boolean; if True, displays a progress bar in the terminal

---

Reference: C. Chandre, B.A. Shadwick, *Hamiltonian fluid reduction of the 1.5D Vlasov–Maxwell equationsn*, [Physics of Plasmas](https://doi.org/10.1063/5.0056155) 28, 092114 (2021); [arXiv:2105.03194](https://arxiv.org/abs/2105.03194)

```bibtex

@article{chandre2021,

         title = {Hamiltonian fluid reduction of the 1.5D Vlasov–Maxwell equations},

         author = {Chandre, C. and Shadwick, B.A.},

         journal = {Physics of Plasmas},

         volume = {28},

         number = {9},

         pages = {092114},

         year = {2021},

         doi = {10.1063/5.0056155},

         URL = {https://doi.org/10.1063/5.0056155}

}

```

    

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