Use OrdinaryDiffEq.jl for timestepping

[charleskawczynski]

We'd like to use OrdinaryDiffEq.jl for time stepping. This will require a lot of work, but I wanted to open an issue for reference. Here's a rough sketch / pseudo code of what we need:

function step!(gm, edmf, ...)

     pre_filter!(gm_model, edmf_model, state, tendencies, ...) # apply pre-aux/state filters
     update_aux!(gm_model, edmf_model, state, tendencies, ...)
     compute_tendencies!(gm_model, edmf_model, state, tendencies, ...)

     # `solve!` will _only_ perform
     #     x = x + Δt * x_tendencies for explicit variables
     #     solve Ax = b for implicit variables (A, b) should be cached at this point.
     # given x, A, b, Δt and x_tendencies
     solve!(gm, edmf, ...) # This will eventually be replaced by calls to OrdinaryDiffEq.jl, with the appropriate tendencies / matrices
     post_filter!(gm_model, edmf_model, state, tendencies, ...) # apply post-aux/state filters
     callbacks!(gm, edmf, ...) # for exporting diagnostics / io
end

function compute_tendencies!(gm_model, edmf_model, state, tendencies, ...)
     # compute grid mean tendencies for all explicit / implicit stepped equations
     compute_material_tendencies!(edmf_model, gm_model, state, tendencies, ...)
end

# This is where all edmf specific functions should live:
function compute_material_tendencies!(edmf_model, gm_model, state, tendencies, ...)
     # compute edmf tendencies for all explicit / implicit stepped equations
end

function update_aux!(gm_model, edmf_model, state, tendencies, ...)
     # Update grid mean aux variables
     update_aux!(edmf_model, gm_model, state, tendencies, ...)
end

function update_aux!(edmf_model, gm_model, state, tendencies, ...)
     # Update edmf aux variables
end