function [UserVar,dhdt]=dhdtExplicit(UserVar,CtrlVar,MUA,F)

Calculates dhdt from flux divergence as

dh/dt = a -  ( dqx/dx + dqy/dy)

[UserVar,dhdt]=dhdtExplicit(UserVar,CtrlVar,MUA,F)

uses u=F.ub, and hence only correct for plug flow, e.g. SSA

Projects the values directly onto nodes.

see also : ProjectFintOntoNodes

ndim=2; dof=1; neq=dof*MUA.Nnodes;

anod=reshape(F.as(MUA.connectivity,1),MUA.Nele,MUA.nod)+reshape(F.ab(MUA.connectivity,1),MUA.Nele,MUA.nod);
hnod=reshape(F.h(MUA.connectivity,1),MUA.Nele,MUA.nod);
unod=reshape(F.ub(MUA.connectivity,1),MUA.Nele,MUA.nod);
vnod=reshape(F.vb(MUA.connectivity,1),MUA.Nele,MUA.nod);


[points,weights]=sample('triangle',MUA.nip,ndim);

b=zeros(MUA.Nele,MUA.nod);


% vector over all elements for each integration point
for Iint=1:MUA.nip


    fun=shape_fun(Iint,ndim,MUA.nod,points) ;
    Deriv=MUA.Deriv(:,:,:,Iint);
    detJ=MUA.DetJ(:,Iint);

    aint=anod*fun;
    hint=hnod*fun;
    uint=unod*fun;
    vint=vnod*fun;

    dhdx=zeros(MUA.Nele,1);
    dhdy=zeros(MUA.Nele,1);
    dudx=zeros(MUA.Nele,1);
    dvdy=zeros(MUA.Nele,1);
    % derivatives at one integration point for all elements
    for Inod=1:MUA.nod

        dhdx=dhdx+Deriv(:,1,Inod).*hnod(:,Inod);
        dhdy=dhdy+Deriv(:,2,Inod).*hnod(:,Inod);

        dudx=dudx+Deriv(:,1,Inod).*unod(:,Inod);
        dvdy=dvdy+Deriv(:,2,Inod).*vnod(:,Inod);

    end

    detJw=detJ*weights(Iint);

    for Inod=1:MUA.nod


        tx=(dhdx.*uint+hint.*dudx);
        ty=(dhdy.*vint+hint.*dvdy);

        term=(aint-tx-ty).*fun(Inod).*detJw;

        b(:,Inod)=b(:,Inod)+term;


    end
end

% assemble right-hand side

rh=sparseUA(neq,1);
for Inod=1:MUA.nod
    rh=rh+sparseUA(MUA.connectivity(:,Inod),ones(MUA.Nele,1),b(:,Inod),neq,1);
end

if ~isfield(MUA,'M')
    MUA.M=MassMatrix2D1dof(MUA);
end

dhdt=MUA.M\rh;
dhdt=full(dhdt);

end

Published with MATLAB® R2018b