--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Euler1d.m	Thu Sep 17 10:12:50 2015 +0200
@@ -0,0 +1,248 @@
+classdef SchmBeam2d < noname.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        N % Number of points total
+        h % Grid spacing
+        u % Grid values
+        x % Values of x and y for each
+        order % Order accuracy for the approximation
+
+        D % non-stabalized scheme operator
+        M % Derivative norm
+        alpha
+
+        H % Discrete norm
+        Hi
+        e_l, e_r
+
+    end
+
+    methods
+        function obj = SchmBeam2d(m,xlim,order,gamma,opsGen)
+            default_arg('opsGen',@sbp.Ordinary);
+            default_arg('gamma', 1.4);
+
+            [x, h] = util.get_grid(xlim{:},m_x);
+
+            ops = opsGen(m_x,h_x,order);
+
+            I_x = speye(m);
+            I_3 = speye(3);
+
+            D1 = sparse(ops.derivatives.D1);
+            H =  sparse(ops.norms.H);
+            Hi = sparse(ops.norms.HI);
+            e_l = sparse(ops.boundary.e_1);
+            e_r = sparse(ops.boundary.e_m);
+
+            D1 = kr(D1, I_3);
+
+            % Norms
+            obj.H = kr(H,I_3);
+
+            % Boundary operators
+            obj.e_l  = kr(e_l,I_3);
+            obj.e_r  = kr(e_r,I_3);
+
+            obj.m = m;
+            obj.h = h;
+            obj.order = order;
+
+
+            % Man har Q_t+F_x=0 i 1D Euler, där
+            % q=[rho, rho*u, e]^T
+            % F=[rho*u, rho*u^2+p, (e+p)*u] ^T
+            % p=(gamma-1)*(e-rho/2*u^2);
+
+
+            %Solving on form q_t + F_x = 0
+            function o = F(q)
+                o = [q(2); q(2).^2/q(1) + p(q); (q(3)+p(q))*q(2)/q(1)];
+            end
+
+            % Equation of state
+            function o = p(q)
+                o = (gamma-1)*(q(3)-q(2).^2/q(1)/2);
+            end
+
+
+            % R =
+            % [sqrt(2*(gamma-1))*rho      , rho                                , rho           ;
+            %  sqrt(2*(gamma-1))*rho*u    , rho*(u+c)                          , rho*(u-c)     ;
+            %  sqrt(2*(gamma-1))*rho*u^2/2, e+(gamma-1)*(e-rho*u^2/2)+rho*u*c, e+(gamma-1)*(e-rho*u^2/2)-rho*u*c]);
+            function o = R(q)
+                rho = q(1);
+                u = q(2)/q(1);
+                e = q(3);
+
+                sqrt2gamm = sqrt(2*(gamma-1));
+
+                o = [
+                     sqrt2gamm*rho      , rho                               , rho                               ;
+                     sqrt2gamm*rho*u    , rho*(u+c)                         , rho*(u-c)                         ;
+                     sqrt2gamm*rho*u^2/2, e+(gamma-1)*(e-rho*u^2/2)+rho*u*c , e+(gamma-1)*(e-rho*u^2/2)-rho*u*c
+                    ];
+            end
+
+            function o = Fx(q)
+                o = zeros(size(q));
+                for i = 1:3:3*m
+                    o(i:i+2) = F(q(i:i+2));
+                end
+            end
+
+
+
+            % A=R*Lambda*inv(R), där Lambda=diag(u, u+c, u-c)     (c är ljudhastigheten)
+            % c^2=gamma*p/rho
+            % function o = A(rho,u,e)
+            % end
+
+
+            obj.D = @Fx;
+            obj.u = x;
+            obj.x = kr(x,ones(3,1));
+        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.
+        %       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.
+        %       neighbour_scheme    is an instance of Scheme that should be interfaced to.
+        %       neighbour_boundary  is a string specifying which boundary to interface to.
+        function [closure, penalty] = boundary_condition(obj,boundary, alpha,data)
+            default_arg('alpha',0);
+            default_arg('data',0);
+
+            % Boundary condition on form
+            %   w_in = w_out + g,       where g is data
+
+            [e,s] = obj.get_boundary_ops(boundary);
+
+            tuning = 1; % ?????????????????????????
+
+            tau = R(q)*lambda(q)*tuning;     % SHOULD THIS BE abs(lambda)?????
+
+            function closure_fun(q,t)
+                q_b = e * q;
+            end
+
+            function penalty_fun(q,t)
+            end
+
+
+
+
+
+            % tau1 < -alpha^2/gamma
+
+            tau1 = tuning * alpha/delt;
+            tau4 = s*alpha;
+
+            sig2 = tuning * alpha/gamm;
+            sig3 = -s*alpha;
+
+            tau = tau1*e+tau4*d3;
+            sig = sig2*d1+sig3*d2;
+
+            closure = halfnorm_inv*(tau*e' + sig*d1');
+
+            pp_e = halfnorm_inv*tau;
+            pp_d = halfnorm_inv*sig;
+            switch class(data)
+                case 'double'
+                    penalty_e = pp_e*data;
+                    penalty_d = pp_d*data;
+                case 'function_handle'
+                    penalty_e = @(t)pp_e*data(t);
+                    penalty_d = @(t)pp_d*data(t);
+                otherwise
+                    error('Wierd data argument!')
+            end
+
+        end
+
+        function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
+            % u denotes the solution in the own domain
+            % v denotes the solution in the neighbour domain
+            [e_u,d1_u,d2_u,d3_u,s_u,gamm_u,delt_u, halfnorm_inv] = obj.get_boundary_ops(boundary);
+            [e_v,d1_v,d2_v,d3_v,s_v,gamm_v,delt_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
+
+            tuning = 2;
+
+            alpha_u = obj.alpha;
+            alpha_v = neighbour_scheme.alpha;
+
+            tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
+            % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning;
+            tau4 = s_u*alpha_u/2;
+
+            sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
+            sig3 = -s_u*alpha_u/2;
+
+            phi2 = s_u*1/2;
+
+            psi1 = -s_u*1/2;
+
+            tau = tau1*e_u  +                     tau4*d3_u;
+            sig =           sig2*d1_u + sig3*d2_u          ;
+            phi =           phi2*d1_u                      ;
+            psi = psi1*e_u                                 ;
+
+            closure =  halfnorm_inv*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
+            penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
+        end
+
+        % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
+        % The right boundary is considered the positive boundary
+        function [e,d1,d2,d3,s,gamm, delt, halfnorm_inv] = get_boundary_ops(obj,boundary)
+            switch boundary
+                case 'w'
+                    e  = obj.e_w;
+                    d1 = obj.d1_w;
+                    d2 = obj.d2_w;
+                    d3 = obj.d3_w;
+                    s = -1;
+                    gamm = obj.gamm_x;
+                    delt = obj.delt_x;
+                    halfnorm_inv = obj.Hix;
+                case 'e'
+                    e  = obj.e_e;
+                    d1 = obj.d1_e;
+                    d2 = obj.d2_e;
+                    d3 = obj.d3_e;
+                    s = 1;
+                    gamm = obj.gamm_x;
+                    delt = obj.delt_x;
+                    halfnorm_inv = obj.Hix;
+                case 's'
+                    e  = obj.e_s;
+                    d1 = obj.d1_s;
+                    d2 = obj.d2_s;
+                    d3 = obj.d3_s;
+                    s = -1;
+                    gamm = obj.gamm_y;
+                    delt = obj.delt_y;
+                    halfnorm_inv = obj.Hiy;
+                case 'n'
+                    e  = obj.e_n;
+                    d1 = obj.d1_n;
+                    d2 = obj.d2_n;
+                    d3 = obj.d3_n;
+                    s = 1;
+                    gamm = obj.gamm_y;
+                    delt = obj.delt_y;
+                    halfnorm_inv = obj.Hiy;
+                otherwise
+                    error('No such boundary: boundary = %s',boundary);
+            end
+        end
+
+        function N = size(obj)
+            N = prod(obj.m);
+        end
+
+    end
+end