view +sbp/+implementations/intOpOP_orders_8to8_ratio2to1.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 4291731570bb
children
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function [IC2F,IF2C,Hc,Hf] = IntOpOP_orders_8to8_ratio2to1(mc,hc,ACC)

% ACC is a string.
% ACC = 'C2F' creates IC2F with one order of accuracy higher than IF2C.
% ACC = 'F2C' creates IF2C with one order of accuracy higher than IC2F.
ratio = 2;
mf = ratio*mc-1;
hf = hc/ratio;

switch ACC
    case 'F2C'
        [stencil_F2C,BC_F2C,HcU,HfU] = ...
        sbp.implementations.intOpOP_orders_8to8_ratio_2to1_accC2F4_accF2C5;
    case 'C2F'
        [stencil_F2C,BC_F2C,HcU,HfU] = ...
        sbp.implementations.intOpOP_orders_8to8_ratio_2to1_accC2F5_accF2C4;
end

stencil_width = length(stencil_F2C);
stencil_hw = (stencil_width-1)/2;
[BC_rows,BC_cols] = size(BC_F2C);

%%% Norm matrices %%%
Hc = speye(mc,mc);
HcUm = length(HcU);
Hc(1:HcUm,1:HcUm) = spdiags(HcU',0,HcUm,HcUm);
Hc(mc-HcUm+1:mc,mc-HcUm+1:mc) = spdiags(rot90(HcU',2),0,HcUm,HcUm);
Hc = Hc*hc;

Hf = speye(mf,mf);
HfUm = length(HfU);
Hf(1:HfUm,1:HfUm) = spdiags(HfU',0,HfUm,HfUm);
Hf(mf-length(HfU)+1:mf,mf-length(HfU)+1:mf) = spdiags(rot90(HfU',2),0,HfUm,HfUm);
Hf = Hf*hf;
%%%%%%%%%%%%%%%%%%%%%%

%%% Create IF2C from stencil and BC
IF2C = sparse(mc,mf);
for i = BC_rows+1 : mc-BC_rows
    IF2C(i,ratio*i-1+(-stencil_hw:stencil_hw)) = stencil_F2C; %#ok<SPRIX>
end
IF2C(1:BC_rows,1:BC_cols) = BC_F2C;
IF2C(end-BC_rows+1:end,end-BC_cols+1:end) = rot90(BC_F2C,2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Create IC2F using symmetry condition %%%%
IC2F = Hf\IF2C.'*Hc;