address feedback from in-person conversation

Author: vchuravy

docs/src/styleguide.md

@@ -20,6 +20,7 @@ conventions, we apply and enforce automated source code formatting
     * The main modified argument comes first. For example, if the right-hand side `du` is modified,
       it should come first. If only the `cache` is modified, e.g., in `prolong2interfaces!`
       and its siblings, put the `cache` first.
+    * Some internal functions take a "computational backend" argument, this should always be passed as the first argument.
     * Otherwise, use the order `mesh, equations, solver, cache`.
     * If something needs to be specified in more detail for dispatch, put the additional argument before the general one
       that is specified in more detail. For example, we use `have_nonconservative_terms(equations), equations`

src/semidiscretization/semidiscretization.jl

@@ -103,7 +103,7 @@ function semidiscretize(semi::AbstractSemidiscretization, tspan;
             storage_type = Array
         end
         if real_type === nothing
-            real_type = Float64
+            real_type = real(semi)
         end
         semi = trixi_adapt(storage_type, real_type, semi)
         if eltype(tspan) !== real_type