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annotate +sbp/D2VariablePeriodic.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 5ccf6aaf6d6b
children bf2554f1825d
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Martin Almquist <malmquist@stanford.edu>
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1 classdef D2VariablePeriodic < sbp.OpSet
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2 properties
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3 D1 % SBP operator approximating first derivative
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4 H % Norm matrix
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5 HI % H^-1
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6 Q % Skew-symmetric matrix
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7 e_l % Left boundary operator
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8 e_r % Right boundary operator
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9 D2 % SBP operator for second derivative
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10 M % Norm matrix, second derivative
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11 d1_l % Left boundary first derivative
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12 d1_r % Right boundary first derivative
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13 m % Number of grid points.
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14 h % Step size
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15 x % grid
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16 borrowing % Struct with borrowing limits for different norm matrices
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17 end
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18
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19 methods
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20 function obj = D2VariablePeriodic(m,lim,order)
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21
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22 x_l = lim{1};
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23 x_r = lim{2};
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24 L = x_r-x_l;
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25 obj.h = L/m;
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26 x = linspace(x_l,x_r,m+1)';
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27 obj.x = x(1:end-1);
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28
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29 switch order
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30
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31 case 6
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32 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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33 obj.e_r, obj.d1_l, obj.d1_r] = ...
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34 sbp.implementations.d2_variable_periodic_6(m,obj.h);
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35 obj.borrowing.M.d1 = 0.1878;
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36 obj.borrowing.R.delta_D = 0.3696;
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37 % Borrowing e^T*D1 - d1 from R
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38
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39 case 4
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40 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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41 obj.e_r, obj.d1_l, obj.d1_r] = ...
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42 sbp.implementations.d2_variable_periodic_4(m,obj.h);
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43 obj.borrowing.M.d1 = 0.2505765857;
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44
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45 obj.borrowing.R.delta_D = 0.577587500088313;
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46 % Borrowing e^T*D1 - d1 from R
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47 case 2
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48 [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
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49 obj.e_r, obj.d1_l, obj.d1_r] = ...
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50 sbp.implementations.d2_variable_periodic_2(m,obj.h);
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51 obj.borrowing.M.d1 = 0.3636363636;
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52 % Borrowing const taken from Virta 2014
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53
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54 obj.borrowing.R.delta_D = 1.000000538455350;
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55 % Borrowing e^T*D1 - d1 from R
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56
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57 otherwise
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58 error('Invalid operator order %d.',order);
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59 end
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60 obj.borrowing.H11 = obj.H(1,1)/obj.h; % First element in H/h,
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61
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62 obj.m = m;
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63 obj.M = [];
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64 end
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65 function str = string(obj)
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66 str = [class(obj) '_' num2str(obj.order)];
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67 end
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68 end
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70
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71 end