Hello DealII's users:
Not obtaining the desired results in two different problems, I would like
to clarify a concept that is the Newton method.
In both cases I want to simulate Navier Stokes equations: the first one is
a time dependent problem (which has an analytical solution) and the second
one is a steady state problem which uses time as a way to get the steady
state, so I will always have a temporal term in the equation.
In both cases, the NS equations are:
du/dt+(u*grad)u-viscosity(grad²)u+(grad)p=0;
(div)u=0;
To implement these equations I use different schemes: coupled method,
pressure projection method, consistent pressure method...
The way I advance in time is the following one:
Assemble the unchanged matrices (i.e. mass matrix, diffusion matrix,
gradient matrix, divergence matrix)
for(unsigned int i=0; i<maximum_num_iterations;i++)
{
step value++;
Assemble the matrices (i.e. convection matrix and right hand side vector)
Solver the linear system (if working with coupled method) or the linear
systems (if working with projection method).
Steady state case: if the residual is less than a tolerance value I give I
stop the loop.
Time dependent problem: I continue until the total time I want to simulate
is reached.
}
I mean, inside this loop, I don't create any inner nonlinear loop such as
it is explained in tutorial step-25 and tutorial step-33. In these
tutorials, inside each temporal iteration, the Newton method is apply.
I am not sure if I must also apply the Newton method in every case since I
always use the convection term in a previous time step or I linearize it
using (u^(n)*gradu)^(n+1). Anyway, it is supposed that convection term is
the only term that introduces a non linearity in the equation, isn't it?
And it is because of it, we should introduce the Newton method to reach
the right solution or on the contrary, I would like to know when and why
we should use Newton method to get the right solution. Is it always
compulsory?
I would be really grateful if you could clarify me this concept.
Thank-you very much in advance.
Isa
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