view +rv/constructDiffOps.m @ 1037:2d7ba44340d0 feature/burgers1d

Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents 44c3ea38097e
children 52f59d27b40f
line wrap: on
line source

function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, g, order, schemeParams, opSet, BCs)
    %% DiffOps for solution vector
    [D, solutionPenalties] = constructTotalFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs);
    D2 = constructSymmetricD2Operator(g, order, opSet);
    D_rv = @(v,viscosity)(D(v) + D2(v, viscosity));

    %% DiffOps for residual viscosity
    [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, g, max(order-2,2), schemeParams, opSet, BCs);
    % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
    % change the sign.
    D_flux = @(v) -D_flux(v);
    % DiffOp for time derivative in residual viscosity
    DvDt = D;
end

function [D, penalties] = constructTotalFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs)
    diffOp = scheme(g, order, schemeParams{:}, opSet);
    [D, penalties]  = addClosuresToDiffOp(diffOp, BCs);
end

function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
    if ~isa(diffOp.D, 'function_handle')
        D = @(v) diffOp.D*v
    else
        D = diffOp.D;
    end
    penalties = cell(size(BCs));
    for i = 1:size(BCs,1)
        for j = 1:size(BCs,2)
            [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
            if ~isa(closure, 'function_handle')
                closure = @(v) closure*v;
            end
            D = @(v) D(v) + closure(v);
        end
    end
end

function D2 = constructSymmetricD2Operator(g, order, opSet)


    m = g.size();
    ops = cell(g.D(),1);
    I = cell(g.D(),1);
    for i = 1:g.D()
       lim = {g.x{i}(1), g.x{i}(end)};
       ops{i} = opSet(m(i), lim, order);
       I{i} = speye(m(i));
    end

    % TBD: How is this generalized to a loop over dimensions or similar?
    switch g.D()
        case 1
            
            e_r = ops{1}.e_r;
            e_l = ops{1}.e_l;
            Hi = ops{1}.HI;
            B = e_r*e_r' - e_l*e_l';
            if isequal(opSet,@sbp.D1Upwind)
                Dm = ops{1}.Dm;
                Dp = ops{1}.Dp;
                D2 = @(viscosity) Dm*spdiag(viscosity)*Dp-Hi*(B*spdiag(viscosity)*Dp);
            else
                D2 = @(viscosity)ops{1}.D2(viscosity);
            end
        case 2
            % TODO: 
            % Currently only implemented for upwind operators.
            % Remove this part once the time-dependent D2 operator is implemented for other opSets
            % or if it is decided that it should only be supported for upwind operators.
            assert(isequal(opSet,@sbp.D1Upwind))
            e_e = kron(ops{1}.e_r,I{2});
            e_w = kron(ops{1}.e_l,I{2});
            Dm_x = kron(ops{1}.Dm,I{2});
            Dp_x  = kron(ops{1}.Dp,I{2});
            H_x  = kron(ops{1}.HI,I{2});
            B_x = e_e*e_e' - e_w*e_w';
            D2_x = @(viscosity) Dm_x*spdiag(viscosity)*Dp_x-H_x*(B_x*spdiag(viscosity)*Dp_x);

            e_n = kron(I{1},ops{2}.e_r);
            e_s = kron(I{1},ops{2}.e_l);
            Dm_y = kron(I{1},ops{2}.Dm);
            Dp_y  = kron(I{1},ops{2}.Dp);
            H_y = kron(I{1},ops{2}.HI);
            B_y = e_n*e_n' - e_s*e_s';
            D2_y = @(viscosity) Dm_y*spdiag(viscosity)*Dp_y-H_y*(B_y*spdiag(viscosity)*Dp_y);
            D2 = @(viscosity)D2_x(viscosity) + D2_y(viscosity);
        otherwise
            error('3D not yet implemented')
    end
    D2 = @(v, viscosity) D2(viscosity)*v;
end