--- a/+scheme/Utux2d.m	Fri Dec 14 18:33:10 2018 +0100
+++ b/+scheme/Utux2d.m	Wed Dec 19 20:00:27 2018 +0100
@@ -27,10 +27,11 @@
 
 
     methods
-         function obj = Utux2d(g ,order, opSet, a)
+         function obj = Utux2d(g ,order, opSet, a, fluxSplitting)
 
             default_arg('a',1/sqrt(2)*[1, 1]);
             default_arg('opSet',@sbp.D2Standard);
+            default_arg('fluxSplitting',[]);
 
             assertType(g, 'grid.Cartesian');
             if iscell(a)
@@ -98,7 +99,13 @@
             obj.h = [ops_x.h ops_y.h];
             obj.order = order;
             obj.a = a;
-            obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
+
+            if (isequal(opSet,@sbp.D1Upwind))
+                obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy + fluxSplitting{1}*obj.DissOpx + fluxSplitting{2}*obj.DissOpy);
+            else
+                obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
+            end
+
         end
         % Closure functions return the opertors applied to the own domain to close the boundary
         % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.