Implement CompressibleEulerPlasma equations

[warisa-r]

The system consists of two conservation laws, one for ions and the other for electrons. An example of these equations is also added.

This is what running elixir_euler_ion_electron.jl yields

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerPlasmaEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                156                run time:       1.35516830e+00 s
 Δt:             6.21881047e-03                └── GC time:    2.30169700e-01 s (16.985%)
 sim. time:      2.00000000e+00 (100.000%)     time/DOF/rhs!:  3.50239101e-07 s
                                               PID:            1.38579241e-06 s
 #DOFs per field:            64                alloc'd memory:        143.465 MiB
 #elements:                  16

 Variable:       rho_ion          rho_v1_ion       rho_e_ion        rho_el           rho_v1_el        rho_e_el
 L2 error:       1.93556997e-02   2.23269846e-02   2.52366595e-02   1.93556997e-02   2.23269846e-02   2.52366595e-02
 Linf error:     2.89596113e-02   3.29344248e-02   4.24609828e-02   2.89596113e-02   3.29344248e-02   4.24609828e-02
 Variable:       rho_ion          v1_ion           p_ion            rho_el           v1_el            p_el
 L2 error prim.: 1.93556997e-02   2.72638095e-03   5.58520892e-03   1.93556997e-02   2.72638095e-03   5.58520892e-03
 Linf error pri.:2.89596113e-02   4.12820033e-03   1.04425919e-02   2.89596113e-02   4.12820033e-03   1.04425919e-02
 ∑∂S/∂U ⋅ Uₜ :  -2.51963484e-03

[github-actions]

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Created with ❤️ by the Trixi.jl community.

[DanielDoehring]

Good first effort!
Seeing this, I would in general opt for implementing the Multi-Ion Euler equations, similar to the Multi-Ion MHD equations. Then, we can derive the Electron-Ion as a special case for this.

[DanielDoehring]

A general comment: Maybe the best idea is to implement at first Multi-Ion Euler in a general fashion, such as done by Andres. Then, we can derive the Electron-Ion system from that as a special case.

[DanielDoehring]

I like the idea of the extracted single species flux. Should be dispatched for the equation type and orientation/normal direction, though.

[warisa-r]

I see. Maybe the implementation of iterating through each ion species (the way ideal_glm_mhd_multiion_2d.jl is handling this aspect) might be more compact. However, if you still think that this is a good idea, I can bring this function back.

[warisa-r]

Good first effort! Seeing this, I would in general opt for implementing the Multi-Ion Euler equations, similar to the Multi-Ion MHD equations. Then, we can derive the Electron-Ion as a special case for this.

Thank you for your detailed feedback! I have implemented the multi-ion system for compressible Euler equations. Is this now more in line with what you had in mind?

Running elixir_euler_multiion.jl yields

────────────────────────────────────────────────────────────────────────────────────────────────────
 Simulation running 'CompressibleEulerMultiIonEquations1D' with DGSEM(polydeg=3)
────────────────────────────────────────────────────────────────────────────────────────────────────
 #timesteps:                197                run time:       8.55753000e-02 s
 Δt:             7.92328612e-03                └── GC time:    0.00000000e+00 s (0.000%)
 sim. time:      2.00000000e+00 (100.000%)     time/DOF/rhs!:  1.84606481e-07 s
                                               PID:            3.91723582e-07 s
 #DOFs per field:            64                alloc'd memory:        158.932 MiB
 #elements:                  16

 Variable:       rho_1            rho_v1_1         rho_e_1          rho_2            rho_v1_2         rho_e_2          rho_3            rho_v1_3         rho_e_3
 L2 error:       2.31589449e-02   2.56244270e-02   2.69083460e-02   9.56221097e-03   1.90514680e-02   3.00279574e-02   2.31589449e-02   2.56244270e-02   2.69083460e-02
 Linf error:     3.31077549e-02   3.76854873e-02   4.56909872e-02   1.53340143e-02   3.08183559e-02   4.70978104e-02   3.31077549e-02   3.76854873e-02   4.56909872e-02
 Variable:       rho_1            v1_1             p_1              rho_2            v1_2             p_2              rho_3            v1_3             p_3
 L2 error prim.: 2.31589449e-02   3.35902165e-03   5.62572214e-03   9.56221097e-03   6.53763949e-03   1.18176493e-02   2.31589449e-02   3.35902165e-03   5.62572214e-03   
 Linf error pri.:3.31077549e-02   6.01291036e-03   1.08211138e-02   1.53340143e-02   1.15000182e-02   2.10914894e-02   3.31077549e-02   6.01291036e-03   1.08211138e-02
 ∑∂S/∂U ⋅ Uₜ :  -2.33315322e-03
────────────────────────────────────────────────────────────────────────────────────────────────────

P.S. The example also works with lax-friedrichs flux.

[DanielDoehring]

Yeah, looking good!

Now we need to find a way to make this system really coupled. Staying for the moment with the ion-only case, you could take a look at the work by Andres

trixi-framework#2213

and implement the ion-ion collision source terms. I am not sure if the testcase itself makes sense, or if you need for this the electron temperature/pressure business.