HallThruster.jl Tutorial¶

HallThruster is an efficient 1D fluid model to simulate Hall Thruster discharges. This interactive tutorial will show you how to get started with HallThruster.jl and will compare our results to the LANDMARK 1-D Hall thruster benchmark. More detailed information about the interface and internals of HallThruster.jl can be found in the Documentation.

To begin, install HallThruster.jl according to the instructions in the README. Then load it:

Let's also load Plots for visualization:

Landmark comparisons¶

Let's try and replicate the LANDMARK benchmarks.

Let us define the function run_landmark() as a helper function. The most important arguments are duration; ncells, nsave, dt. When increasing the amount of cells, the timestep has to be reduced accordingly to satisfy the CFL condition. nsave specifies the amount of times the solution is saved in constant time intervals.

Here we have the Landmark source terms and energy loss terms given as a standard, and we can select one of the 3 test cases to run. We initialize a new simulation and define the domain as twice the thruster length, as evident by the argument domain = (0.0, 0.05). The default flux is the rusanov flux. Grids may be even or uneven. To generate an even grid with ncells cells, create an EvenGrid Uneven grids may be employed by passing an UnevenGrid object instead of an EvenGrid object. This allows you to either use a grid you generated yourself, to use an uneven grid generated using the default density function, or use a density function of your own.

Now we can use run_landmark() to perform simulations of our desired cases.

sol_case_1 is a Solution object, which has the following fields

• t: The times at which the solution was saved
• u: A vector of solution matrices of length nsave. This contains the main state variables: $\rho_n$, $\rho_i$ and $\rho_i u_i$
• savevals: A vector of NamedTuples containing some auxilliary variables including $\phi$, $n_e$, $T_{ev}$, $\nu_{AN}$ , $\nu_{en}$, $\nu_{ei}$, and $\mu$
• retcode: A short symbol describing how the solution ended. Generally this should be :success.
• params: The params that the simulation was run with.

HallThruster has some built-in plotting and postprocessing faculties. First, if we have Plots loaded, we can type plot(sol, frame) to plot the solution at the given frame (an Int from 1:nsave). Leaving out frame will plot the last frame by default.

We can load in the LANDMARK data for comparison:

This looks quite different than the benchmark. However, Hall thrusters are strongly oscillatory devices, and we only plotted the last frame. Let's look instead at the time averaged behavior. For this, we use the time_average function, which returns another Solution object, and plot that against the benchmark.

This looks better. There are discrepancies due to minor differences in physics model and choice of numerics, but overall the agreement is good. We can also check the other LANDMARK cases. Below is the time-averaged behavior of case 2:

And case 3: