Mercurial > repos > public > sbplib

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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 cda996e64925
children
line wrap: on
line source

%%  Function that constructs artificial dissipation operators using undivided differences
function D = dissipationOperator(m, order, Hinv, scaling)
    % TBD: Add or remove D_2 and Dp/Dm?
    % d2=[1 2 1];
    % D_2=(diag(ones(m-1,1),-1)-2*diag(ones(m,1),0)+ ...
    % diag(ones(m-1,1),1));
    % D_2(1,1:3)=[d2];D_2(m,m-2:m)=[d2];
    % %Dm
    % DD_m=(diag(ones(m-1,1),+1)-diag(ones(m,1),0));
    % DD_m(m,m-1:m)=[-1 1];
    % %Dp
    % DD_p=(-diag(ones(m-1,1),-1)+diag(ones(m,1),0));
    % DD_p(1,1:2)=[-1 1];

    switch order
        case 1
            DD_1=(diag(ones(m-1,1),+1)-diag(ones(m,1),0));
            DD_1(m,m-1:m)=[-1 1];
            D = DD_2'*DD_2;
        case 2
            dd2=0*[1 -2 1];
            DD_2=(diag(ones(m-1,1),-1)-2*diag(ones(m,1),0)+ ...
            	  diag(ones(m-1,1),1));
            DD_2(1,1:3)=[dd2];DD_2(m,m-2:m)=[dd2];
            D = DD_2'*DD_2;
        case 3
            d3=0*[-1 3 -3 1];
            DD_3=(-diag(ones(m-2,1),-2)+3*diag(ones(m-1,1),-1)-3*diag(ones(m,1),0)+ ...
                  diag(ones(m-1,1),1));
            DD_3(1:2,1:4)=[d3;d3];
            DD_3(m,m-3:m)=[d3];
            D = DD_3'*DD_3;
        case 4
            default_arg('scaling', 1/12);
            d4=0*[1 -4 6 -4 1];
            DD_4=(diag(ones(m-2,1),2)-4*diag(ones(m-1,1),1)+6*diag(ones(m,1),0)-4*diag(ones(m-1,1),-1)+diag(ones(m-2,1),-2));
            DD_4(1:2,1:5)=[d4;d4];DD_4(m-1:m,m-4:m)=[d4;d4];
            D = DD_4'*DD_4;
        case 5
            d5=0*[-1 5 -10 10 -5 1];
            DD_5=(-diag(ones(m-3,1),-3)+5*diag(ones(m-2,1),-2)-10*diag(ones(m-1,1),-1)+10*diag(ones(m,1),0)-5*diag(ones(m-1,1),1)+diag(ones(m-2,1),2));
            DD_5(1:3,1:6)=[d5;d5;d5];
            DD_5(m-1:m,m-5:m)=[d5;d5];
            D = DD_5'*DD_5; 
        case 6
            default_arg('scaling', 1/60);
            d6=0*[1 -6 15 -20 15 -6 1];
            DD_6=(diag(ones(m-3,1),3)-6*diag(ones(m-2,1),2)+15*diag(ones(m-1,1),1)-20*diag(ones(m,1),0)+15*diag(ones(m-1,1),-1)-6*diag(ones(m-2,1),-2)+diag(ones(m-3,1),-3));
            DD_6(1:3,1:7)=[d6;d6;d6];DD_6(m-2:m,m-6:m)=[d6;d6;d6];
            D = DD_6'*DD_6;
        case 7
            d7=0*[-1 7 -21 35 -35 21 -7 1]; 
            DD_7=(-diag(ones(m-4,1),-4)+7*diag(ones(m-3,1),-3)-21*diag(ones(m-2,1),-2)+35*diag(ones(m-1,1),-1)-35*diag(ones(m,1),0)+21*diag(ones(m-1,1),1)-7*diag(ones(m-2,1),2)+diag(ones(m-3,1),3));
            DD_7(1:4,1:8)=[d7;d7;d7;d7];
            DD_7(m-2:m,m-7:m)=[d7;d7;d7];
            D = DD_7'*DD_7;
        case 9
            d9=0*[-1 9 -36 84 -126 126 -84 36 -9 1]; 
            DD_9=(-diag(ones(m-5,1),-5)+9*diag(ones(m-4,1),-4)-36*diag(ones(m-3,1),-3)+84*diag(ones(m-2,1),-2)-126*diag(ones(m-1,1),-1)+126*diag(ones(m,1),0)-84*diag(ones(m-1,1),1)+36*diag(ones(m-2,1),2)-9*diag(ones(m-3,1),3)+diag(ones(m-4,1),4));
            DD_9(1:5,1:10)=[d9;d9;d9;d9;d9];
            DD_9(m-3:m,m-9:m)=[d9;d9;d9;d9];
            D = DD_9'*DD_9;
        otherwise
            error('Order not yet supported', order);
    end
    D = scaling*sparse(Hinv*D);
end