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annotate +sbp/+implementations/d1_gauss_4.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 0bc37a25ed88
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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409
42c4f0b545d6 Remove m as input to implementation function. Fix error message for invalid m to D1Gauss
Jonatan Werpers <jonatan@werpers.com>
parents: 408
diff changeset
1 function [D1,H,x,h,e_l,e_r] = d1_gauss_4(L)
405
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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2
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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3 % L: Domain length
434
0bc37a25ed88 Bug fix sbp in time gauss default arg
Martin Almquist <martin.almquist@it.uu.se>
parents: 409
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4 default_arg('L',1);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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5
409
42c4f0b545d6 Remove m as input to implementation function. Fix error message for invalid m to D1Gauss
Jonatan Werpers <jonatan@werpers.com>
parents: 408
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6 N = 4;
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Martin Almquist <martin.almquist@it.uu.se>
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7
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Martin Almquist <martin.almquist@it.uu.se>
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8 % Quadrature nodes on interval [-1, 1]
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Martin Almquist <martin.almquist@it.uu.se>
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9 x = [ -0.8611363115940526; -0.3399810435848563; 0.3399810435848563; 0.8611363115940526];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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10
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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11 % Shift nodes to [0,L]
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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12 x = (x+1)/2*L;
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Martin Almquist <martin.almquist@it.uu.se>
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13
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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14 % Boundary extrapolation operators
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
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15 e_l = [1.5267881254572668; -0.8136324494869273; 0.4007615203116504; -0.1139171962819899];
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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16 e_r = flipud(e_l);
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Martin Almquist <martin.almquist@it.uu.se>
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17 e_l = sparse(e_l);
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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18 e_r = sparse(e_r);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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19
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Martin Almquist <martin.almquist@it.uu.se>
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20 %%%% Compute approximate h %%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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21 h = L/(N-1);
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Martin Almquist <martin.almquist@it.uu.se>
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22 %%%%%%%%%%%%%%%%%%%%%%%%%
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23
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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24 %%%% Norm matrix on [-1,1] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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25 P = sparse(N,N);
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Martin Almquist <martin.almquist@it.uu.se>
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26 P(1,1) = 0.3478548451374539;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 P(2,2) = 0.6521451548625461;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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28 P(3,3) = 0.6521451548625461;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 P(4,4) = 0.3478548451374539;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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30 %%%%%%%%%%%%%%%%%%%%%%%%%
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31
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Martin Almquist <martin.almquist@it.uu.se>
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32 %%%% Norm matrix on [0,L] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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33 H = P*L/2;
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Martin Almquist <martin.almquist@it.uu.se>
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34 %%%%%%%%%%%%%%%%%%%%%%%%%
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parents:
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35
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Martin Almquist <martin.almquist@it.uu.se>
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36 %%%% D1 on [-1,1] %%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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37 D1 = sparse(N,N);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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38 D1(1,1) = -3.3320002363522817;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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39 D1(1,2) = 4.8601544156851962;
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40 D1(1,3) = -2.1087823484951789;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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41 D1(1,4) = 0.5806281691622644;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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42
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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43 D1(2,1) = -0.7575576147992339;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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44 D1(2,2) = -0.3844143922232086;
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parents:
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45 D1(2,3) = 1.4706702312807167;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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46 D1(2,4) = -0.3286982242582743;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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47
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Martin Almquist <martin.almquist@it.uu.se>
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48 D1(3,1) = 0.3286982242582743;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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49 D1(3,2) = -1.4706702312807167;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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50 D1(3,3) = 0.3844143922232086;
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Jonatan Werpers <jonatan@werpers.com>
parents: 405
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51 D1(3,4) = 0.7575576147992339;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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52
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 D1(4,1) = -0.5806281691622644;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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54 D1(4,2) = 2.1087823484951789;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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55 D1(4,3) = -4.8601544156851962;
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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56 D1(4,4) = 3.3320002363522817;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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57 %%%%%%%%%%%%%%%%%%%%%%%%%
4d9d8064e58b Implementation of D1 based on Gauss quadrature formula with 4 nodes.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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58
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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59 % D1 on [0,L]
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Martin Almquist <martin.almquist@it.uu.se>
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60 D1 = D1*2/L;