view +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 1031:2ef20d00b386 feature/advectionRV

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 b19e142fcae1
children
line wrap: on
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function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_4_min_boundary_points(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 4:de ordn. SBP Finita differens         %%%
    %%% operatorer framtagna av Mark Carpenter  %%%
    %%%                                         %%%
    %%% H           (Normen)                    %%%
    %%% D1=H^(-1)Q  (approx f?rsta derivatan)   %%%
    %%% D2          (approx andra derivatan)    %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %H?r med endast 4 randpunkter


    BP = 4;
    if(m<2*BP)
        error(['Operator requires at least ' num2str(2*BP) ' grid points']);
    end


    % Norm
    Hv = ones(m,1);
    Hv(1:4) = [17/48 59/48 43/48 49/48];
    Hv(m-3:m) = rot90(Hv(1:4),2);
    Hv = h*Hv;
    H = spdiag(Hv, 0);
    HI = spdiag(1./Hv, 0);


    % Boundary operators
    e_l = sparse(m,1);
    e_l(1) = 1;
    e_r = rot90(e_l, 2);

    d1_l = sparse(m,1);
    d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
    d1_r = -rot90(d1_l, 2);

    d2_l = sparse(m,1);
    d2_l(1:4) = 1/h^2*[2 -5 4 -1];
    d2_r = rot90(d2_l, 2);

    d3_l = sparse(m,1);
    d3_l(1:4) = 1/h^3*[-1 3 -3 1];
    d3_r = -rot90(d3_l, 2);


    % First derivative
    stencil = [1/12 -2/3 0 2/3 -1/12];
    diags = [-1 0 1];

    Q_U = [
        0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
         -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
         0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
         0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
    ];

    Q = stripeMatrix(stencil, diags, m);
    Q(1:4,1:4)=Q_U;
    Q(m-3:m,m-3:m) = -rot90(Q_U, 2);

    D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');

    % Fourth derivative
    stencil = [-1/6, 2, -13/2, 28/3, -13/2, 2, -1/6];
    diags = -3:3;
    M4 = stripeMatrix(stencil, diags, m);

    M4_U=[
        0.8e1/0.3e1 -0.37e2/0.6e1 0.13e2/0.3e1 -0.5e1/0.6e1;
        -0.37e2/0.6e1 0.47e2/0.3e1 -13 0.11e2/0.3e1;
        0.13e2/0.3e1 -13 0.44e2/0.3e1 -0.47e2/0.6e1;
        -0.5e1/0.6e1 0.11e2/0.3e1 -0.47e2/0.6e1 0.29e2/0.3e1;
    ];


    M4(1:4,1:4) = M4_U;
    M4(m-3:m,m-3:m) = rot90(M4_U, 2);
    M4 = 1/h^3*M4;

    D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
end