Mercurial > repos > public > sbplib
view +sbp/+implementations/d2_variable_periodic_6.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> |
---|---|
date | Thu, 17 Jan 2019 10:25:06 +0100 |
parents | bbf303c1f0cf |
children |
line wrap: on
line source
function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_6(m,h) % m = number of unique grid points, i.e. h = L/m; if(m<7) error(['Operator requires at least ' num2str(7) ' grid points']); end % Norm Hv = ones(m,1); Hv = h*Hv; H = spdiag(Hv, 0); HI = spdiag(1./Hv, 0); % Dummy boundary operators e_l = sparse(m,1); e_r = rot90(e_l, 2); d1_l = sparse(m,1); d1_r = -rot90(d1_l, 2); % D1 operator diags = -3:3; stencil = [-1/60 9/60 -45/60 0 45/60 -9/60 1/60]; D1 = stripeMatrixPeriodic(stencil, diags, m); D1 = D1/h; % D2 operator scheme_width = 7; scheme_radius = (scheme_width-1)/2; r = 1:m; offset = scheme_width; r = r + offset; function D2 = D2_fun(c) c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ]; Mm3 = c(r-2)/0.40e2 + c(r-1)/0.40e2 - 0.11e2/0.360e3 * c(r-3) - 0.11e2/0.360e3 * c(r); Mm2 = c(r-3)/0.20e2 - 0.3e1/0.10e2 * c(r-1) + c(r+1)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r-2); Mm1 = -c(r-3)/0.40e2 - 0.3e1/0.10e2 * c(r-2) - 0.3e1/0.10e2 * c(r+1) - c(r+2)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r-1); M0 = c(r-3)/0.180e3 + c(r-2)/0.8e1 + 0.19e2/0.20e2 * c(r-1) + 0.19e2/0.20e2 * c(r+1) + c(r+2)/0.8e1 + c(r+3)/0.180e3 + 0.101e3/0.180e3 * c(r); Mp1 = -c(r-2)/0.40e2 - 0.3e1/0.10e2 * c(r-1) - 0.3e1/0.10e2 * c(r+2) - c(r+3)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r+1); Mp2 = c(r-1)/0.20e2 - 0.3e1/0.10e2 * c(r+1) + c(r+3)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r+2); Mp3 = c(r+1)/0.40e2 + c(r+2)/0.40e2 - 0.11e2/0.360e3 * c(r) - 0.11e2/0.360e3 * c(r+3); vals = [Mm3,Mm2,Mm1,M0,Mp1,Mp2,Mp3]; diags = -scheme_radius : scheme_radius; M = spdiagsPeriodic(vals,diags); M=M/h; D2=HI*(-M ); end D2 = @D2_fun; end