Time accuracy order of Vlasov Ampere

[liyz92]

Time accuracy order of Vlasov Ampere

[liyz92]

ex_order_T=0.1.pdf
ex_order_T=1.pdf

[pnavaro]

Thanks for reporting this, could you share the code to reproduce this problem ?

[liyz92]

liyz2.zip
Thanks.
steps:

1. run strong_landau_damping.jl in notebooks to get reference solution, dt = 0.001, steps = 1000. save 'ex' at T=1 by ex_all_0_001 = propagator.e_dofs[1]
2. comment lines 64, 65, 66, 67 to store initial data.
3. in line 173 of strong_landau_damping.jl, set dt = 0.01, steps = 100, then run strong_landau_damping.jl, then save 'ex' at T=1 by ex_all_0_01 = propagator.e_dofs[1].
4. in line 173, set dt = 0005, steps = 200, then run strong_landau_damping.jl, then save 'ex' at T=1 by ex_all_0_005 = propagator.e_dofs[1].
5. get the order of 'ex' by (ex_all_0_001 .- ex_all_0_01)./(ex_all_0_001 .- ex_all_0_005).
6. we can also plot((ex_all_0_001 .- ex_all_0_01)./(ex_all_0_001 .- ex_all_0_005)) to the order.

[pnavaro]

I am with my kids at home due to the lockdown but I'll do my best.

[liyz92]

Thank you so much. I am also checking it now.

[liyz92]

After commenting solve_poisson!( efield_poisson, particle_group, kernel_smoother0, maxwell_solver, rho) in the loop,
second order can be obtained, and very small energy error is also obtained. This function updates e_dofs[1] by solving Poisson equation, but in the splitting method, e_dofs[1] is updated by solving Ampere equation. In the code, these two approaches are equivalent only when the integral average of Ex is 0.

[pnavaro]

updating e_dofs[1] by solving Poisson equation should not be there. I'll take a look.

[pnavaro]

It is because you set

e_dofs = [ efield_poisson, zeros(nx), zeros(nx)]

e_dofs[1] is a reference of efield_poisson, you should instead do

e_dofs = [ zeros(x), zeros(nx), zeros(nx)]
e_dofs[1] .= efield_poisson

e_dofs[1] is a copy of efield_poisson and a different array

[liyz92]

Ok, I see. Thanks. That explains why the values of e_dofs[1] are also updated after running solve poisson equation (which updates efield_poisson).