Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 1031:2ef20d00b386 feature/advectionRV
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> |
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date | Thu, 17 Jan 2019 10:25:06 +0100 |
parents | b19e142fcae1 |
children |
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function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_4_min_boundary_points(m,h) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% 4:de ordn. SBP Finita differens %%% %%% operatorer framtagna av Mark Carpenter %%% %%% %%% %%% H (Normen) %%% %%% D1=H^(-1)Q (approx f?rsta derivatan) %%% %%% D2 (approx andra derivatan) %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %H?r med endast 4 randpunkter BP = 4; if(m<2*BP) error(['Operator requires at least ' num2str(2*BP) ' grid points']); end % Norm Hv = ones(m,1); Hv(1:4) = [17/48 59/48 43/48 49/48]; Hv(m-3:m) = rot90(Hv(1:4),2); Hv = h*Hv; H = spdiag(Hv, 0); HI = spdiag(1./Hv, 0); % Boundary operators e_l = sparse(m,1); e_l(1) = 1; e_r = rot90(e_l, 2); d1_l = sparse(m,1); d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3]; d1_r = -rot90(d1_l, 2); d2_l = sparse(m,1); d2_l(1:4) = 1/h^2*[2 -5 4 -1]; d2_r = rot90(d2_l, 2); d3_l = sparse(m,1); d3_l(1:4) = 1/h^3*[-1 3 -3 1]; d3_r = -rot90(d3_l, 2); % First derivative stencil = [1/12 -2/3 0 2/3 -1/12]; diags = [-1 0 1]; Q_U = [ 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2; -0.59e2/0.96e2 0 0.59e2/0.96e2 0; 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2; 0.1e1/0.32e2 0 -0.59e2/0.96e2 0; ]; Q = stripeMatrix(stencil, diags, m); Q(1:4,1:4)=Q_U; Q(m-3:m,m-3:m) = -rot90(Q_U, 2); D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r'); % Fourth derivative stencil = [-1/6, 2, -13/2, 28/3, -13/2, 2, -1/6]; diags = -3:3; M4 = stripeMatrix(stencil, diags, m); M4_U=[ 0.8e1/0.3e1 -0.37e2/0.6e1 0.13e2/0.3e1 -0.5e1/0.6e1; -0.37e2/0.6e1 0.47e2/0.3e1 -13 0.11e2/0.3e1; 0.13e2/0.3e1 -13 0.44e2/0.3e1 -0.47e2/0.6e1; -0.5e1/0.6e1 0.11e2/0.3e1 -0.47e2/0.6e1 0.29e2/0.3e1; ]; M4(1:4,1:4) = M4_U; M4(m-3:m,m-3:m) = rot90(M4_U, 2); M4 = 1/h^3*M4; D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r'); end