Covariant Advection in DGMulti#111
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benegee
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I did an initial, very superficial review, because honestly I do not know much about the math and the DGMulti code you used.
| # OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed | ||
| # callbacks | ||
| sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), | ||
| dt = 1.0, save_everystep = true, callback = callbacks) |
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You could use ode_default_options() here.
| @unpack u_values, aux_quad_values = cache | ||
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| # interpolate u, du to quadrature points | ||
| du_values = similar(u_values) # TODO: DGMulti. Can we move this to the analysis cache somehow? |
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Is this a general TODO that is addressed somewhere else?
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I copied this over from the corresponding Trixi function. I will add a note pointing to Trixi somehow
| end | ||
| aux_values[i, element] = SVector{n_aux}(aux_node) | ||
| end | ||
| # TODO: implement Christoffel symbols |
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Christoffel values are not yet used for this PR, so I left them out, because they can't be tested for now.
| # Construct a DGMultiMesh consisting of prismatic elements based on a refined icosahedron | ||
| # As of now this 3D mesh only serves to simulate 2D covariant equations on the sphere, with | ||
| # the spherical shell thus only consisting of a single layer of prismatic elements extruded | ||
| # from the triangular faces of the icosahedron. |
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Is the described "abuse" of the 3D mesh temporary to try out things? I would be absolutely fine with this.
If it is supposed to become permanent at some point, some comments in the code could be helpful for anyone trying to implement a similar construction.
| local_values_threaded = [Trixi.allocate_nested_array(uEltype, nvars, (rd.Nq,), dg) | ||
| for _ in 1:Threads.nthreads()] |
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This pattern is currently under discussion because, IIRC, it will not work with Julia 1.12 anymore.
| @reexport import Trixi: waterheight | ||
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| # DGMulti solvers | ||
| using StartUpDG: RefElemData, MeshData, AbstractElemShape |
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Are all of these needed in this PR, or maybe in some upcoming PR?
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## main #111 +/- ##
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This PR adds a covariant solver for DGMulti and a function constructing an icosahedral DGMultiMesh using prism elements, which are used in the new elixir
elixir_spherical_advection_covariant_prismed_icosahedron.jl.