--- a/+scheme/Utux.m	Mon Jan 07 16:32:40 2019 +0100
+++ b/+scheme/Utux.m	Mon Jan 07 16:35:04 2019 +0100
@@ -5,6 +5,9 @@
         grid % Grid
         order % Order accuracy for the approximation
 
+        a % Wave speed
+          % Can either be a constant or function handle.
+
         H % Discrete norm
         D
 
@@ -12,13 +15,21 @@
         Hi
         e_l
         e_r
-        v0
     end
 
 
     methods
-        function obj = Utux(g, order, opSet)
+        function obj = Utux(g, order, opSet, a, fluxSplitting)
             default_arg('opSet',@sbp.D2Standard);
+            default_arg('a',1);
+            default_arg('fluxSplitting',[]);
+
+            assertType(g, 'grid.Cartesian');
+            if isa(a, 'function_handle')
+                obj.a = spdiag(grid.evalOn(g, a));
+            else
+                obj.a = a;
+            end
 
             m = g.size();
             xl = g.getBoundary('l');
@@ -26,7 +37,15 @@
             xlim = {xl, xr};
 
             ops = opSet(m, xlim, order);
-            obj.D1 = ops.D1;
+
+            if (isequal(opSet, @sbp.D1Upwind))
+                obj.D1 = (ops.Dp + ops.Dm)/2;
+                DissOp = (ops.Dm - ops.Dp)/2;
+                obj.D = -(obj.a*obj.D1 + fluxSplitting*DissOp);
+            else 
+                obj.D1 = ops.D1;
+                obj.D = -obj.a*obj.D1;
+            end
 
             obj.grid = g;
 
@@ -35,12 +54,10 @@
 
             obj.e_l = ops.e_l;
             obj.e_r = ops.e_r;
-            obj.D = -obj.D1;
 
             obj.m = m;
             obj.h = ops.h;
             obj.order = order;
-
         end
         % Closure functions return the opertors applied to the own doamin 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.
@@ -51,8 +68,24 @@
         %       neighbour_boundary  is a string specifying which boundary to interface to.
         function [closure, penalty] = boundary_condition(obj,boundary,type)
             default_arg('type','dirichlet');
-            tau =-1*obj.e_l;
-            closure = obj.Hi*tau*obj.e_l';
+            sigma_left = -1; % Scalar penalty parameter for left boundary
+            sigma_right = 1; % Scalar penalty parameter for right boundary
+            switch boundary
+                % Can only specify boundary condition where there is inflow
+                % Extract the postivie resp. negative part of a, for the left
+                % resp. right boundary, and set other values of a to zero.
+                % Then the closure will effectively only contribute to inflow boundaries
+                case {'l','L','left','Left'}
+                    a_inflow = obj.a;
+                    a_inflow(a_inflow < 0) = 0;
+                    tau = sigma_left*a_inflow*obj.e_l;
+                    closure = obj.Hi*tau*obj.e_l';
+                case {'r','R','right','Right'}
+                    a_inflow = obj.a;
+                    a_inflow(a_inflow > 0) = 0;
+                    tau = sigma_right*a_inflow*obj.e_r;
+                    closure = obj.Hi*tau*obj.e_r';
+            end
             penalty = -obj.Hi*tau;
 
          end
@@ -61,11 +94,11 @@
              switch boundary
                  % Upwind coupling
                  case {'l','left'}
-                     tau = -1*obj.e_l;
+                     tau = -1*obj.a*obj.e_l;
                      closure = obj.Hi*tau*obj.e_l';
                      penalty = -obj.Hi*tau*neighbour_scheme.e_r';
                  case {'r','right'}
-                     tau = 0*obj.e_r;
+                     tau = 0*obj.a*obj.e_r;
                      closure = obj.Hi*tau*obj.e_r';
                      penalty = -obj.Hi*tau*neighbour_scheme.e_l';
              end