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view +sbp/D2VariablePeriodic.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents 5ccf6aaf6d6b
children bf2554f1825d
line wrap: on
line source

classdef D2VariablePeriodic < sbp.OpSet
    properties
        D1 % SBP operator approximating first derivative
        H % Norm matrix
        HI % H^-1
        Q % Skew-symmetric matrix
        e_l % Left boundary operator
        e_r % Right boundary operator
        D2 % SBP operator for second derivative
        M % Norm matrix, second derivative
        d1_l % Left boundary first derivative
        d1_r % Right boundary first derivative
        m % Number of grid points.
        h % Step size
        x % grid
        borrowing % Struct with borrowing limits for different norm matrices
    end

    methods
        function obj = D2VariablePeriodic(m,lim,order)

            x_l = lim{1};
            x_r = lim{2};
            L = x_r-x_l;
            obj.h = L/m;
            x = linspace(x_l,x_r,m+1)';
            obj.x = x(1:end-1);

            switch order

                case 6
                    [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                        obj.e_r, obj.d1_l, obj.d1_r] = ...
                        sbp.implementations.d2_variable_periodic_6(m,obj.h);
                    obj.borrowing.M.d1 = 0.1878;
                    obj.borrowing.R.delta_D = 0.3696;
                    % Borrowing e^T*D1 - d1 from R

                case 4
                    [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                        obj.e_r, obj.d1_l, obj.d1_r] = ...
                        sbp.implementations.d2_variable_periodic_4(m,obj.h);
                    obj.borrowing.M.d1 = 0.2505765857;

                    obj.borrowing.R.delta_D = 0.577587500088313;
                    % Borrowing e^T*D1 - d1 from R
                case 2
                    [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                        obj.e_r, obj.d1_l, obj.d1_r] = ...
                        sbp.implementations.d2_variable_periodic_2(m,obj.h);
                    obj.borrowing.M.d1 = 0.3636363636; 
                    % Borrowing const taken from Virta 2014

                    obj.borrowing.R.delta_D = 1.000000538455350;
                    % Borrowing e^T*D1 - d1 from R
                    
                otherwise
                    error('Invalid operator order %d.',order);
            end
            obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,

            obj.m = m;
            obj.M = [];
        end
        function str = string(obj)
            str = [class(obj) '_' num2str(obj.order)];
        end
    end


end