Fix interpolation with VelocityAveraging

[efaulhaber]

Based on #1037.

When interpolating the initial state or after restarting from files (especially when interpolating from VTK files in postprocessing), velocity averaging is not initialized correctly, which leads to zero wall velocity even if the structure is moving. With this PR, interpolation from VTK files in postprocessing works as intended.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 90.13%. Comparing base (4b44813) to head (740ed27).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1235      +/-   ##
==========================================
- Coverage   90.14%   90.13%   -0.01%     
==========================================
  Files         138      138              
  Lines       10803    10797       -6     
==========================================
- Hits         9738     9732       -6     
  Misses       1065     1065              

Flag	Coverage Δ
total	90.14% <100.00%> (-0.01%)	⬇️
unit	76.47% <100.00%> (+0.04%)	⬆️

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[svchb]

Suggested change

	foreach_system(semi) do system
	initialize_averaged_velocity!(system, v0_ode, semi, tspan[1])
	end
	foreach_system(semi_new) do system
	initialize_averaged_velocity!(system, v0_ode, semi_new, tspan[1])
	end

This initializes the adapted semidiscretization that is stored in ode.p.semi.

[svchb]

Suggested change

	return cb(integrator)
	if semi.integrate_tlsph[]
	foreach_system(semi) do system
	initialize_averaged_velocity!(system, v_ode, semi, t)
	end
	end
	return cb(integrator)

This resets the averaged velocity when each integrator starts; the regression test shows that a second regular integration otherwise keeps data from the first run.

[svchb]

Suggested change

	return DiscreteCallback(update_averaged_velocity_callback!,
	update_averaged_velocity_callback!,
	initialize=(initialize_averaged_velocity_callback!),
	save_positions=(false, false))
	end
	return DiscreteCallback(update_averaged_velocity_callback!,
	update_averaged_velocity_callback!,
	initialize=(initialize_averaged_velocity_callback!),
	save_positions=(false, false))
	end
	# `initialize`
	function initialize_averaged_velocity_callback!(cb, vu_ode, t, integrator)
	v_ode, u_ode = vu_ode.x
	semi = integrator.p.semi
	foreach_system(semi) do system
	initialize_averaged_velocity!(system, v_ode, semi, t)
	end
	return cb
	end

This resets the averaged velocity when each split integrator starts; the regression test shows that a second split integration otherwise keeps the old velocity and time.

[svchb]

Add using OrdinaryDiffEqLowStorageRK at the top of test/schemes/structure/total_lagrangian_sph/velocity_averaging.jl, then add this inside the existing Velocity Averaging test set:

@testset "Reinitialize averaged velocity for integration" begin
    algorithm = CarpenterKennedy2N54(williamson_condition=false)
    callbacks = (("update", () -> UpdateCallback()),
                 ("split", () -> SplitIntegrationCallback(algorithm; dt=0.01)))

    for (name, callback) in callbacks
        @testset "$name integration" begin
            velocity_averaging = VelocityAveraging(time_constant=0.5)
            system = velocity_averaging_test_system(; velocity_averaging)
            semi = Semidiscretization(system, neighborhood_search=nothing)
            ode = semidiscretize(semi, (0.0, 0.1))
            system = ode.p.semi.systems[1]

            TrixiParticles.SciMLBase.solve(ode, algorithm; dt=0.01, adaptive=false,
                                          callback=callback(), save_everystep=false)

            @test system.cache.t_last_averaging[] == last(ode.tspan)

            TrixiParticles.SciMLBase.init(ode, algorithm; dt=0.01, adaptive=false,
                                         callback=callback(), save_everystep=false)

            @test system.cache.t_last_averaging[] == first(ode.tspan)
            @test system.cache.averaged_velocity == [1.0 3.0 5.0
                                                     2.0 4.0 6.0]
        end
    end
end

This reproduces stale data for both regular and split integration: three assertions fail with the current changes, while all twenty-one tests pass when both initialization hooks are restored.