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annotate +sbp/+implementations/d1_upwind_4.m @ 314:88584b0cfba1 feature/beams

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Corrections and clean up order 4
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 23 Sep 2016 22:55:30 +0200
parents f7ac3cd6eeaa
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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Martin Almquist <martin.almquist@it.uu.se>
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1 function [H, HI, Dp, Dm, e_1, e_m] = d1_upwind_4(m,h)
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2
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3 if(m<8)
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4 error('Operator requires at least 8 grid points');
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5 end
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6
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7 Hv=ones(m,1);
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8 Hv(1:4)=[49/144 61/48 41/48 149/144];
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9 Hv(m-3:m)=rot90(Hv(1:4),2);
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10 Hv = Hv*h;
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11 H = spdiag(Hv,0);
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12 HI = spdiag(1./Hv,0);
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13
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14 q_diags = [-1, 0, 1, 2 3];
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15 q_stencil = [-1/4 -5/6 3/2 -1/2 1/12];
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16 Qp = stripeMatrix(q_stencil, q_diags,m);
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17
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18 Q_U = [
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19 -0.1e1/0.48e2 0.205e3/0.288e3 -0.29e2/0.144e3 0.1e1/0.96e2;
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20 -0.169e3/0.288e3 -0.11e2/0.48e2 0.33e2/0.32e2 -0.43e2/0.144e3;
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21 0.11e2/0.144e3 -0.13e2/0.32e2 -0.29e2/0.48e2 0.389e3/0.288e3;
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22 0.1e1/0.32e2 -0.11e2/0.144e3 -0.65e2/0.288e3 -0.13e2/0.16e2;
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23 ];
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24
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25 Qp(1:4,1:4)=Q_U;
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26 Qp(m-3:m,m-3:m)=rot90(Q_U, 2)'; %%% This is different from standard SBP
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28 Qm=-Qp';
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30 e_1=sparse(m,1);e_1(1)=1;
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31 e_m=sparse(m,1);e_m(m)=1;
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33 Dp=HI*(Qp-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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35 Dm=HI*(Qm-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
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36 end