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view +sbp/+implementations/d4_lonely_6_3.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 b19e142fcae1
children
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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_6_3(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 6:te ordn. SBP Finita differens         %%%
    %%% operatorer med diagonal norm            %%%
    %%% Extension to variable koeff             %%%
    %%%                                         %%%
    %%% H           (Normen)                    %%%
    %%% D1=H^(-1)Q  (approx f?rsta derivatan)   %%%
    %%% D2          (approx andra derivatan)    %%%
    %%% D2=HI*(R+C*D*S                          %%%
    %%%                                         %%%
    %%% R=-D1'*H*C*D1-RR                        %%%
    %%%                                         %%%
    %%% RR ?r dissipation)                      %%%
    %%% Dissipationen uppbyggd av D4:           %%%
    %%% DI=D4*B*H*D4                            %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % H?r med 7 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator
    % Denna ?r noggrannare, och har 2a ordningens randdslutning och b?r ge 6te
    % ordningens konvergens. Hade 2 fria parametrar att optimera

    % Norm
    Hv = ones(m,1);
    Hv(1:7) = [0.414837907e9/0.1191965760e10, 0.475278367e9/0.397321920e9, 0.13872751e8/0.12416310e8, 0.346739027e9/0.595982880e9, 0.560227469e9/0.397321920e9, 0.322971631e9/0.397321920e9, 0.616122491e9/0.595982880e9];
    Hv(m-6:m) = rot90(Hv(1:7),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(1:6) = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h;
    d1_r = -rot90(d1_l, 2);

    d2_l = sparse(m,1);
    d2_l(1:6) = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2;
    d2_r = rot90(d2_l, 2);

    d3_l = sparse(m,1);
    d3_l(1:6) = [-0.17e2/0.4e1 0.71e2/0.4e1 -0.59e2/0.2e1 0.49e2/0.2e1 -0.41e2/0.4e1 0.7e1/0.4e1;]/h^3;
    d3_r = -rot90(d3_l, 2);


    % Fourth derivative, 1th order accurate at first 8 boundary points
    stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240];
    diags = -4:4;
    M4 = stripeMatrix(stencil, diags, m);

    M4_U = [
        0.1399708478939e13/0.263487168000e12 -0.13482796013041e14/0.834376032000e12 0.344344095859e12/0.17565811200e11 -0.3166261424681e13/0.250312809600e12 0.1508605165681e13/0.333750412800e12 -0.486270829441e12/0.834376032000e12 -0.221976356359e12/0.5006256192000e13;
        -0.13482796013041e14/0.834376032000e12 0.7260475818391e13/0.139062672000e12 -0.27224036353e11/0.406022400e9 0.1847477458951e13/0.41718801600e11 -0.848984558161e12/0.55625068800e11 0.247494925991e12/0.139062672000e12 0.165585445559e12/0.834376032000e12;
        0.344344095859e12/0.17565811200e11 -0.27224036353e11/0.406022400e9 0.2044938640393e13/0.22250027520e11 -0.1071086785417e13/0.16687520640e11 0.502199537033e12/0.22250027520e11 -0.143589154441e12/0.55625068800e11 -0.88181965559e11/0.333750412800e12;
        -0.3166261424681e13/0.250312809600e12 0.1847477458951e13/0.41718801600e11 -0.1071086785417e13/0.16687520640e11 0.628860435593e12/0.12515640480e11 -0.73736245829e11/0.3337504128e10 0.195760572271e12/0.41718801600e11 -0.81156046361e11/0.250312809600e12;
        0.1508605165681e13/0.333750412800e12 -0.848984558161e12/0.55625068800e11 0.502199537033e12/0.22250027520e11 -0.73736245829e11/0.3337504128e10 0.76725285869e11/0.4450005504e10 -0.3912429433e10/0.406022400e9 0.53227370659e11/0.17565811200e11;
        -0.486270829441e12/0.834376032000e12 0.247494925991e12/0.139062672000e12 -0.143589154441e12/0.55625068800e11 0.195760572271e12/0.41718801600e11 -0.3912429433e10/0.406022400e9 0.1699707221791e13/0.139062672000e12 -0.6959018412841e13/0.834376032000e12;
        -0.221976356359e12/0.5006256192000e13 0.165585445559e12/0.834376032000e12 -0.88181965559e11/0.333750412800e12 -0.81156046361e11/0.250312809600e12 0.53227370659e11/0.17565811200e11 -0.6959018412841e13/0.834376032000e12 0.3012195053939e13/0.263487168000e12;
    ];

    M4(1:7,1:7) = M4_U;
    M4(m-6:m,m-6: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