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comparison +sbp/upwind4.m @ 52:4f5a65f49035

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Fixed the upwind operators.
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 11 Nov 2015 15:43:15 -0800
parents ebd25e5a481a
children
comparison
equal deleted inserted replaced
51:0be702829bb9 52:4f5a65f49035
1 function [H, HI, Dp, Dm, e_1, e_m] = upwind4(m,h) 1 function [H, HI, Dp, Dm, e_1, e_m] = upwind4(m,h)
2 2
3 H=spdiag(ones(m,1),0); 3 Hv=ones(m,1);
4 H(1:4,1:4)=spdiag([49/144 61/48 41/48 149/144]); 4 Hv(1:4)=[49/144 61/48 41/48 149/144];
5 H(m-3:m,m-3:m)=fliplr(flipud(spdiag([49/144 61/48 41/48 149/144]))); 5 Hv(m-3:m)=rot90(Hv(1:4),2);
6 H=H*h; 6 Hv = Hv*h;
7 HI=inv(H); 7 H = spdiag(Hv,0);
8 HI = spdiag(1./Hv,0);
8 9
10 q_diags = [-1, 0, 1, 2 3];
11 q_stencil = [-1/4 -5/6 3/2 -1/2 1/12];
12 Qp = stripeMatrix(q_stencil, q_diags,m);
9 13
10 Qp=(-1/4*spdiag(ones(m-1,1),-1)-5/6*spdiag(ones(m,1),0)+3/2*spdiag(ones(m-1,1),+1)-1/2*spdiag(ones(m-2,1),+2)+1/12*spdiag(ones(m-3,1),+3)); 14 Q_U = [
11 %Q_U = [-0.49e2 / 0.2640e4 0.11167e5 / 0.15840e5 -0.1541e4 / 0.7920e4 0.43e2 / 0.5280e4; -0.9403e4 / 0.15840e5 -0.551e3 / 0.2640e4 0.1779e4 / 0.1760e4 -0.2311e4 / 0.7920e4; 0.659e3 / 0.7920e4 -0.751e3 / 0.1760e4 -0.1541e4 / 0.2640e4 0.21287e5 / 0.15840e5; 0.51e2 / 0.1760e4 -0.551e3 / 0.7920e4 -0.3683e4 / 0.15840e5 -0.713e3 / 0.880e3;]; 15 -0.1e1/0.48e2 0.205e3/0.288e3 -0.29e2/0.144e3 0.1e1/0.96e2;
12 %Q_U = [-0.29e2 / 0.1680e4 0.7067e4 / 0.10080e5 -0.961e3 / 0.5040e4 0.23e2 / 0.3360e4; -0.6023e4 / 0.10080e5 -0.331e3 / 0.1680e4 0.1119e4 / 0.1120e4 -0.1451e4 / 0.5040e4; 0.439e3 / 0.5040e4 -0.491e3 / 0.1120e4 -0.961e3 / 0.1680e4 0.13507e5 / 0.10080e5; 0.31e2 / 0.1120e4 -0.331e3 / 0.5040e4 -0.2383e4 / 0.10080e5 -0.453e3 / 0.560e3;]; 16 -0.169e3/0.288e3 -0.11e2/0.48e2 0.33e2/0.32e2 -0.43e2/0.144e3;
13 17 0.11e2/0.144e3 -0.13e2/0.32e2 -0.29e2/0.48e2 0.389e3/0.288e3;
14 Q_U = [-0.1e1 / 0.48e2 0.205e3 / 0.288e3 -0.29e2 / 0.144e3 0.1e1 / 0.96e2; -0.169e3 / 0.288e3 -0.11e2 / 0.48e2 0.33e2 / 0.32e2 -0.43e2 / 0.144e3; 0.11e2 / 0.144e3 -0.13e2 / 0.32e2 -0.29e2 / 0.48e2 0.389e3 / 0.288e3; 0.1e1 / 0.32e2 -0.11e2 / 0.144e3 -0.65e2 / 0.288e3 -0.13e2 / 0.16e2;]; 18 0.1e1/0.32e2 -0.11e2/0.144e3 -0.65e2/0.288e3 -0.13e2/0.16e2;
19 ];
15 20
16 Qp(1:4,1:4)=Q_U; 21 Qp(1:4,1:4)=Q_U;
17 Qp(m-3:m,m-3:m)=flipud( fliplr(Q_U(1:4,1:4) ) )'; %%% This is different from standard SBP 22 Qp(m-3:m,m-3:m)=rot90(Q_U,2)'; %%% This is different from standard SBP
18 23
19 Qm=-Qp'; 24 Qm=-Qp';
20 25
21 e_1=zeros(m,1);e_1(1)=1; 26 e_1=sparse(m,1);e_1(1)=1;
22 e_m=zeros(m,1);e_m(m)=1; 27 e_m=sparse(m,1);e_m(m)=1;
23 28
24 Dp=HI*(Qp-1/2*e_1*e_1'+1/2*e_m*e_m') ; 29 Dp=HI*(Qp-1/2*e_1*e_1'+1/2*e_m*e_m') ;
25 30
26 Dm=HI*(Qm-1/2*e_1*e_1'+1/2*e_m*e_m') ; 31 Dm=HI*(Qm-1/2*e_1*e_1'+1/2*e_m*e_m') ;
27 end 32 end