Hi developers and users,
does Libmesh provide two methods to assemble the Ke_ij and Fe_i?
the examples 6&8 about wave equation take the Me_ij*u_tt+Ce*u_t+Ke*u=f,
while the convection-diffustion equation of exmaples 9-10 take
\tilde{Ke}*u=f instead of Ce*u_t+Ke*u=f, and \tilde{Ke} contains the
time rate term.
I understand both method should work perfect, but why providing two
different implement method for time-dependent problem, does it depend on
the order of time rate? if my equation is 1st-order rate PDE, which
iuput method is better.
anther question is about the coefficient 0.5*dt in the exmaples 9-10, I
can't understand the physical meaning of this 0.5. what will happen if
we modify this parameter?
I am a newbie so many boring questions, thanks for your all kindness!
Liang
copy from the example 9.
*for* (*unsigned* *int* i=0; i<phi.size(); i++)
{
Fe(i) += JxW[qp]*(
u_old*phi[i][qp] +
-.5*dt*(
(grad_u_old*velocity)*phi[i][qp] +
0.01*(grad_u_old*dphi[i][qp]))
);
*for* (*unsigned* *int* j=0; j<phi.size(); j++)
{
Ke(i,j) += JxW[qp]*(
phi[i][qp]*phi[j][qp] +
.5*dt*(
(velocity*dphi[j][qp])*phi[i][qp] +
0.01*(dphi[i][qp]*dphi[j][qp]))
);
}
}
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