--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Burgers1d	Thu Jan 17 11:03:22 2019 +0100
@@ -0,0 +1,148 @@
+classdef Burgers1d < scheme.Scheme
+    properties
+        grid % Physical grid
+        order % Order accuracy for the approximation
+        
+        params
+
+        D % Non-stabalized scheme operator
+        H % Discrete norm
+        Hi % Norm inverse
+        e_l
+        e_r
+        d_l
+        d_r
+    end
+
+    methods
+        function obj = Burgers1d(grid, pde_form, operator_type, order, dissipation, params)
+            assert(grid.D == 1);
+            assert(grid.size() == length(params.eps));
+            m = grid.size();
+            lim = grid.lim{1}; % Ugly, and only applicable for cartesian grids.
+            switch operator_type
+                case 'narrow'
+                    ops = sbp.D4Variable(m, lim, order);
+                    D1 = ops.D1;
+                    D2 = ops.D2;
+                    if (strcmp(dissipation,'on'))
+                        DissipationOp = -1*sbp.dissipationOperator(m, order, ops.HI);
+                    end
+                    d_l = ops.d1_l';
+                    d_r = ops.d1_r';
+                case 'upwind-'
+                    ops = sbp.D1Upwind(m, lim, order);
+                    D1 = (ops.Dp + ops.Dm)/2;
+                    D2 = @(eps) ops.Dp*spdiag(eps)*ops.Dm;
+                    if (strcmp(dissipation,'on'))
+                        DissipationOp = (ops.Dp-ops.Dm)/2;
+                    end
+                    d_l = ops.e_l'*ops.Dm;
+                    d_r = ops.e_r'*ops.Dm;
+                case 'upwind+'
+                    ops = sbp.D1Upwind(m, lim, order);
+                    D1 = (ops.Dp + ops.Dm)/2;
+                    D2 = @(eps) ops.Dm*spdiag(eps)*ops.Dp;
+                    if (strcmp(dissipation,'on'))
+                        DissipationOp = (ops.Dp-ops.Dm)/2;
+                    end
+                    d_l = ops.e_l'*ops.Dp;
+                    d_r = ops.e_r'*ops.Dp;
+                case 'upwind+-'
+                    ops = sbp.D1Upwind(m, lim, order);
+                    D1 = (ops.Dp + ops.Dm)/2;
+                    D2 = @(eps) (ops.Dp*spdiag(eps)*ops.Dm + ops.Dm*spdiag(eps)*ops.Dp)/2;
+                    if (strcmp(dissipation,'on'))
+                        DissipationOp = (ops.Dp-ops.Dm)/2;
+                    end
+                    d_l = ops.e_l'*D1;
+                    d_r = ops.e_r'*D1;
+                otherwise
+                    error('Other operator types not yet supported', operator_type);
+            end
+
+            switch pde_form
+                case 'skew-symmetric'
+                    if (strcmp(dissipation,'on'))
+                        D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
+                    else
+                        D = @(v, viscosity) - 1/3*D1*v.^2 + (-1/3*v.*D1 + D2(params.eps + viscosity))*v;
+                    end
+                case 'conservative'
+                    if (strcmp(dissipation,'on'))
+                        D = @(v, viscosity) -1/2*D1*v.^2 + (D2(params.eps + viscosity) + max(abs(v))*DissipationOp)*v;
+                    else
+                        D = @(v, viscosity) -1/2*D1*v.^2 + D2(params.eps + viscosity)*v;
+                    end
+                otherwise
+                    error('Not supported', pde_form);
+            end
+
+            obj.grid = grid;
+            obj.order = order;
+            obj.params = params;
+
+            obj.D = D;
+            obj.H =  ops.H;
+            obj.Hi = ops.HI;
+            obj.e_l = ops.e_l;
+            obj.e_r = ops.e_r;
+            obj.d_l =  d_l;
+            obj.d_r =  d_r;
+        end
+
+        % Closure functions return the operators applied to the own doamin to close the boundary
+        % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other domain.
+        %       boundary            is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
+        %       type                is a string specifying the type of boundary condition if there are several.
+        %       data                is a function returning the data that should be applied at the boundary.
+        function [closure, penalty] = boundary_condition(obj,boundary,type,data)
+            default_arg('type','robin');
+            default_arg('data',0);
+            [e, d, i_b, s] = obj.get_boundary_ops(boundary);
+            switch type
+                % Stable robin-like boundary conditions ((u+-abs(u))*u/3 - eps*u_x)) with +- at left/right boundary
+                case {'R','robin'}
+                    p = s*obj.Hi*e;
+                    closure = @(v, viscosity) p*(((v(i_b)-s*abs(v(i_b)))/3)*(v(i_b)) - ((obj.params.eps(i_b) + viscosity(i_b))*d*v));
+                    switch class(data)
+                        case 'double'
+                            penalty = s*p*data;
+                        case 'function_handle'
+                            penalty = @(t) s*p*data(t);
+                        otherwise
+                            error('Wierd data argument!')
+                    end
+                otherwise
+                    error('No such boundary condition: type = %s',type);
+            end
+        end
+
+        % Ruturns the boundary ops, boundary index and sign for the boundary specified by the string boundary.
+        % The right boundary is considered the positive boundary
+        function [e, d, i_b, s] = get_boundary_ops(obj,boundary)
+            switch boundary
+                case 'l'
+                    e = obj.e_l;
+                    d = obj.d_l;
+                    i_b = 1;
+                    s = -1;
+                case 'r'
+                    e = obj.e_r;
+                    d = obj.d_r;
+                    i_b = length(e);
+                    s = 1;
+                otherwise
+                    error('No such boundary: boundary = %s',boundary);
+            end
+        end
+
+        function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
+            error('An interface function does not exist yet');
+        end
+
+        function N = size(obj)
+            N = obj.grid.m;
+        end
+    end
+end
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