--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/SbpOperators/volumeops/derivatives/dissipation.jl	Fri Feb 10 08:36:56 2023 +0100
@@ -0,0 +1,107 @@
+"""
+    undivided_skewed04(g::EquidistantGrid, p, direction)
+
+Create undivided difference operators approximating the `p`th derivative. The
+operators do not satisfy any SBP-property and are meant to be used for
+building artificial dissipation terms.
+
+The operators and how they are used to create accurate artifical dissipation
+is described in "K. Mattsson, M. Svärd, and J. Nordström, “Stable and Accurate
+Artificial Dissipation,” Journal of Scientific Computing, vol. 21, no. 1, pp.
+57–79, Aug. 2004"
+"""
+function undivided_skewed04(g::EquidistantGrid, p, direction)
+    T = eltype(g)
+    interior_weights = T.(dissipation_interior_weights(p))
+
+    D  = stencil_operator_distinct_closures(
+        g,
+        dissipation_interior_stencil(interior_weights),
+        dissipation_lower_closure_stencils(interior_weights),
+        dissipation_upper_closure_stencils(interior_weights),
+        direction,
+    )
+    Dᵀ = stencil_operator_distinct_closures(
+        g,
+        dissipation_transpose_interior_stencil(interior_weights),
+        dissipation_transpose_lower_closure_stencils(interior_weights),
+        dissipation_transpose_upper_closure_stencils(interior_weights),
+        direction,
+    )
+
+    return D, Dᵀ
+end
+
+undivided_skewed04(g::EquidistantGrid{1}, p) = undivided_skewed04(g, p, 1)
+
+function dissipation_interior_weights(p)
+   if p == 0
+       return (1,)
+   end
+
+   return (0, dissipation_interior_weights(p-1)...) .- (dissipation_interior_weights(p-1)..., 0)
+end
+
+midpoint(weights) = length(weights)÷2 + 1
+midpoint_transpose(weights) = length(weights)+1 - midpoint(weights)
+
+function dissipation_interior_stencil(weights)
+    return Stencil(weights..., center=midpoint(weights))
+end
+function dissipation_transpose_interior_stencil(weights)
+    if iseven(length(weights))
+        weights = map(-, weights)
+    end
+
+    return Stencil(weights..., center=midpoint_transpose(weights))
+end
+
+dissipation_lower_closure_size(weights) = midpoint(weights) - 1
+dissipation_upper_closure_size(weights) = length(weights) - midpoint(weights)
+
+function dissipation_lower_closure_stencils(interior_weights)
+    stencil(i) = Stencil(interior_weights..., center=i)
+    return ntuple(i->stencil(i), dissipation_lower_closure_size(interior_weights))
+end
+
+function dissipation_upper_closure_stencils(interior_weights)
+    center(i) = length(interior_weights) - dissipation_upper_closure_size(interior_weights) + i
+    stencil(i) = Stencil(interior_weights..., center=center(i))
+    return ntuple(i->stencil(i), dissipation_upper_closure_size(interior_weights))
+end
+
+function dissipation_transpose_lower_closure_stencils(interior_weights)
+    closure = ntuple(i->dissipation_transpose_lower_closure_stencil(interior_weights, i), length(interior_weights))
+
+    N = maximum(s->length(s.weights), closure)
+    return right_pad.(closure, N)
+end
+
+function dissipation_transpose_upper_closure_stencils(interior_weights)
+    closure = reverse(ntuple(i->dissipation_transpose_upper_closure_stencil(interior_weights, i), length(interior_weights)))
+
+    N = maximum(s->length(s.weights), closure)
+    return left_pad.(closure, N)
+end
+
+
+function dissipation_transpose_lower_closure_stencil(interior_weights, i)
+    w = ntuple(k->interior_weights[i], dissipation_lower_closure_size(interior_weights))
+
+    for k ∈ i:-1:1
+        w = (w..., interior_weights[k])
+    end
+
+    return Stencil(w..., center = i)
+end
+
+function dissipation_transpose_upper_closure_stencil(interior_weights, i)
+    j = length(interior_weights)+1-i
+    w = ntuple(k->interior_weights[j], dissipation_upper_closure_size(interior_weights))
+
+    for k ∈ j:1:length(interior_weights)
+        w = (interior_weights[k], w...)
+    end
+
+    return Stencil(w..., center = length(interior_weights)-midpoint(interior_weights)+1)
+end