Implement the time integration method used in DualSPHysics and add docs for time integration #716
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This was referenced Feb 11, 2025
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Feb 13, 2025
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| This approach allows us to use specialized time integration methods that do not work with | ||
| general `ODEProblem`s. |
| ### [Leapfrog kick-drift-kick](@id kick_drift_kick) | ||
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| The kick-drift-kick scheme of the leapfrog method, updating positions ``u`` | ||
| and velocities ``v`` with the functions ``\operatorname{kick}`` and ``\operatorname{drift}``, |
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Function kick below is (u,v, t) here it is (u,t) this difference should be explained
| ### Symplectic position Verlet | ||
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| When the density is integrated (with [`ContinuityDensity`](@ref)), the density is appended | ||
| to ``v`` as additional dimension, so all previously mentioned schemes treat the density |
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| to ``v`` as additional dimension, so all previously mentioned schemes treat the density | |
| to ``v`` as an additional dimension, so all previously mentioned schemes treat the density |
| The SPH code [DualSPHysics](https://github.com/DualSPHysics/DualSPHysics) implements | ||
| a variation of the drift-kick-drift scheme where the density is updated separately. | ||
| In the following, we will call the derivative of the density ``R(v, u, t)``, | ||
| even though it is actually included in the ``\operatorname{kick}`` as additional dimension. |
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| even though it is actually included in the ``\operatorname{kick}`` as additional dimension. | |
| even though it is actually included in the ``\operatorname{kick}`` as an additional dimension. |
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| Note that the method `VelocityVerlet` does not work with TrixiParticles.jl for the same and | ||
| other additional reasons. |
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Weird jump. Please include the explanation in the previous text. Also redundant because of the warning below.
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| uprev, uprev2, f, t, | ||
| dt, reltol, p, calck, |
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| uprev, uprev2, f, t, | |
| dt, reltol, p, calck, | |
| uprev, uprev2, f, t, dt, reltol, p, calck, |
| tTypeNoUnits} | ||
| # We only use inplace functions in TrixiParticles, so there is no point | ||
| # in implementing the non-inplace version. | ||
| error("`SymplecticPositionVerlet` only supports inplace functions") |
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| error("`SymplecticPositionVerlet` only supports inplace functions") | |
| error("`SymplecticPositionVerlet` supports only in-place functions.") |
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| # verify_f2(integrator.f.f2, integrator.k[2].x[2], duprev, uprev, integrator.p, | ||
| # integrator.t, integrator, cache) |
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| # verify_f2(integrator.f.f2, integrator.k[2].x[2], duprev, uprev, integrator.p, | |
| # integrator.t, integrator, cache) |
| @@ -171,6 +171,13 @@ @Article{Bonet1999 | |||
| publisher = {Elsevier BV}, | |||
| } | |||
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Also cite a DualSPHysics paper in which this is explained.
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Supersedes #693.
Closes #683.
Find the rendered docs for this PR here:
https://trixi-framework.github.io/TrixiParticles.jl/previews/PR716/