Move special fd stencils to lbmpy

.gitignore

@@ -11,5 +11,6 @@ _build
 /.idea
 _local_tmp
 **/.vscode
+/lbmpy_tests/db
 doc/bibtex.json
-/html_doc
+/html_doc
\ No newline at end of file

lbmpy/phasefield/fd_stencils.py

+import sympy as sp
+
+from pystencils.fd.spatial import fd_stencils_standard
+
+
+def fd_stencils_isotropic_high_density_code(indices, dx, fa):
+    dim = fa.field.spatial_dimensions
+    if dim == 1:
+        return fd_stencils_standard(indices, dx, fa)
+    elif dim == 2:
+        order = len(indices)
+
+        if order == 1:
+            idx = indices[0]
+            assert 0 <= idx < 2
+            other_idx = 1 if indices[0] == 0 else 0
+            weights = {-1: sp.Rational(1, 12) / dx,
+                       0: sp.Rational(1, 3) / dx,
+                       1: sp.Rational(1, 12) / dx}
+            upper_terms = sum(fa.neighbor(idx, +1).neighbor(other_idx, off) * w for off, w in weights.items())
+            lower_terms = sum(fa.neighbor(idx, -1).neighbor(other_idx, off) * w for off, w in weights.items())
+            return upper_terms - lower_terms
+        elif order == 2:
+            if indices[0] == indices[1]:
+                idx = indices[0]
+                diagonals = sp.Rational(1, 8) * sum(fa.neighbor(0, i).neighbor(1, j) for i in (-1, 1) for j in (-1, 1))
+                div_direction = sp.Rational(1, 2) * sum(fa.neighbor(idx, i) for i in (-1, 1))
+                center = - sp.Rational(3, 2) * fa
+                return (diagonals + div_direction + center) / (dx ** 2)
+            else:
+                return fd_stencils_standard(indices, dx, fa)
+    raise NotImplementedError("Supports only derivatives up to order 2 for 1D and 2D setups")