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GPU RHS 1 : Sources (not collisions)
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# Geometry (x, v\_x) | ||
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The `geoemtryXVx` folder contains all the code describing methods which are specific to a geometry with 1 spatial dimension and 1 velocity dimension. It is broken up into the following sub-folders: | ||
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<!-- - [boltzmann](./botzmann/README.md) - --> | ||
- [geometry](./geometry/README.md) --> - All the dimension tags used for a simulation in the geometry. | ||
<!-- - [initialization](./initialization/README.md) - --> | ||
- [poisson](./poisson/README.md) - Code describing the polar Poisson solver. | ||
<!-- - [rhs](./rhs/README.md) - Code describing the operators on the right hand side of the Boltzmann equation; namely sources, sinks and collisions.--> | ||
<!-- - [time_integration](./time_integration/README.md) - --> | ||
<!-- - [utils](./utils/README.md) - --> | ||
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The `geometryXVx` folder contains all the code describing methods which are specific to a geometry with 1 spatial dimension and 1 velocity dimension. It is broken up into the following sub-folders: | ||
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- [boltzmann](./boltzmann/README.md) : Solvers for a Boltzmann equation. | ||
- [geometry](./geometry/README.md) : All the dimension tags used for a simulation in the geometry. | ||
- [initialization](./initialization/README.md) : Initialization methods for the distribution function. | ||
- [poisson](./poisson/README.md) : Code describing the polar Poisson solver. | ||
- [rhs](./rhs/README.md) : Code describing the operators on the right hand side of the Boltzmann equation; namely sources, sinks and collisions. | ||
- [time_integration](./time_integration/README.md) : Time integrators for a Boltzmann-Poisson system of equations. | ||
- [utils](./utils/README.md) : Miscellaneous utility functions. |
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# Boltzmann solver | ||
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The `boltzmann` folder contains methods for solving a Boltzmann equation. Such methods typically take the distribution function and the electric field computed at a given time $t$, and return the value of the distribution function at a time $t+dt$, where $dt$ is the timestep of the simulation. A Boltzmann equation refers to an advection equation in phase space with sources. In the simplified 1D geometry in space and velocity it has the general form | ||
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$\partial_t f + v \partial_x f + \frac{E}{m}\, \partial_v f = S(f)$ | ||
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Where $f$ is the distribution function, $x$ and $v$ are the space and velocity variables respectively, $E$ is the electric field and $m$ is the mass of the considered plasma species. The $S(f)$ operator refers to any source terms (including collisions). When taking $S(f)=0$ this equation is often referred to as a Vlasov equation. | ||
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The implemented Boltzmann solvers are: | ||
- SplitRightHandSideSolver | ||
- SplitVlasovSolver |
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# Initializatin methods | ||
# Initialization methods | ||
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Initialization methods define the value of the distribution function at the start of the simulation. For instance, these methods allows for initializing the distribution function as a perturbed maxwellian, or to read the values from a previous simulation. | ||
The initialization folder contains any methods that define the value of the distribution function at the start of the simulation. | ||
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The implemented initialization methods are: | ||
- BumpontailEquilibrium | ||
- MaxwellianEquilibrium | ||
- RestartInitialization | ||
- SingleModePerturbInitialization |
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