Add advection Vec equivalent

docs/src/ascii.md

@@ -15,12 +15,13 @@ Some users may have trouble entering unicode characters like ⋆ or ∂ in their
 
 ## Vector Calculus Equivalents
 
-| Vec     | DEC        | How to enter               |
-| ------- | ---------- | -------------------------- |
-| grad    | d          | grad                       |
-| div     | ∘(⋆,d,⋆)   | div                        |
-| curl    | ∘(d,⋆)     | curl                       |
-| ∇       | d          | \nabla                     |
-| ∇ᵈ      | ∘(⋆,d,⋆)   | \nabla \<tab\> \\^d \<tab\> |
-| ∇x      | ∘(d,⋆)     | \nabla \<tab\> x           |
+| Vec      | DEC              | How to enter                |
+| -------- | ---------------- | --------------------------  |
+| grad     | d                | grad                        |
+| div      | ∘(⋆,d,⋆)         | div                         |
+| curl     | ∘(d,⋆)           | curl                        |
+| ∇        | d                | \nabla                      |
+| ∇ᵈ       | ∘(⋆,d,⋆)         | \nabla \<tab\> \\^d \<tab\> |
+| ∇x       | ∘(d,⋆)           | \nabla \<tab\> x            |
+| adv(X,Y) | ∘(⋆,d,⋆)(X∧Y)    | adv                         |
 

src/decapodeacset.jl

@@ -731,5 +731,24 @@ vec_to_dec_op2 = Pair{Symbol, Symbol}[]
 
 Replace Vector Calculus operators with Discrete Exterior Calculus equivalents.
 """
-vec_to_dec!(d::SummationDecapode) = replace_names!(d, vec_to_dec_op1, vec_to_dec_op2)
+function vec_to_dec!(d::SummationDecapode)
+  # Perform simple substitutions.
+  replace_names!(d, vec_to_dec_op1, vec_to_dec_op2)
+
+  # Replace `adv` with divergence of ∧.
+  advs = incident(d, :adv, :op2)
+  adv_tgts = d[advs, :res]
+
+  # Intermediate wedges.
+  wedge_tgts = add_parts!(d, :Var, length(adv_tgts), name=map(i -> Symbol("•_adv_$i"), eachindex(advs)), type=:infer)
+  # Divergences.
+  add_parts!(d, :Op1, length(adv_tgts), src=wedge_tgts, tgt=adv_tgts, op1=fill([:⋆,:d,:⋆],length(advs)))
+  # Point advs to the intermediates.
+  d[collect(advs), :res] = wedge_tgts
+
+  # Replace adv with ∧.
+  d[collect(advs), :op2] = fill(:∧,length(advs))
+
+  d
+end
 

test/diag2dwd.jl

@@ -1229,5 +1229,30 @@ end
   vec_to_dec!(t7)
   t7 = contract_operators(t7)
   @test only(t7[:op1]) == [:d,:⋆,:d,:⋆]
+
+  # Test advection is divergence of wedge product.
+  t8 = @decapode begin
+    A == adv(B, C)
+  end
+  vec_to_dec!(t8)
+
+  @test only(t8[:op1]) == [:⋆,:d,:⋆]
+  @test only(t8[:op2]) == :∧
+
+  # Test multiple advections.
+  t9 = @decapode begin
+    A == adv(B, C)
+    D == adv(E, F)
+  end
+  vec_to_dec!(t9)
+
+  t9_expected = @decapode begin
+    A == ∘(⋆,d,⋆)(B ∧ C)
+    D == ∘(⋆,d,⋆)(E ∧ F)
+  end
+  t9_expected[incident(t9_expected, Symbol("•1"), :name), :name] = Symbol("•_adv_1")
+  t9_expected[incident(t9_expected, Symbol("•2"), :name), :name] = Symbol("•_adv_2")
+  @test is_isomorphic(t9, t9_expected)
+
 end