[petsc-users] Rescaling quantites to remove positivity constraints

[Mani Chandra]

Hi,

I'm trying to solve for fluid flows with large density and pressure
variations using the theta method in the TS module. This inevitably leads
to negative densities and pressures during the course of the evolution. In
order to deal with this, I am trying to now solve for log(rho) and log(P)
instead of rho and P. In order to do this, I changed my initial conditions
for rho and P to log(rho) and log(P) and inside the residual evaluation
function I keep the original code unchanged expect that I add the following
lines above the original code:

rho = exp(logrho)
P = exp(logP)

since I expect the solution vector x[j][i] to now have logrho and logP
instead of rho and  P. I now run the simulation with a modified newton
krylov method and lag the jacobian for every 100 linear solves. The
jacobian assembly is using colored finite differences. This goes smoothly
from the point I start the simulation to the first 100 linear solves after
which it needs to assemble the jacobian again. At this point the nonlinear
solver crashes and I think something is wrong with the jacobian assembly. I
checked that the simulation runs till it has to assemble the jacobian the
second time by varying the lagging by say 10, 20, 30, ... It fails
everytime it has to assemble the second time.

 When I view the solution using VecView inside TSMonitor during the time
elasped when the simulation ran, the initial conditions are log(rho) and
log(P) but the output of the vector actually has rho and P and not log(rho)
and log(P) which I expect the solver to be solving for. However when I look
at the .vts files generated by -ts_monitor_solution_vtk, the output is
log(rho) and log(P).

Should I be doing something else in order to rescale the quantities that
TS/SNES should solve for instead of what I did above?

The method suggesting that one rescales is described in this paper:
"A newton-krylov solver for implicit solution of hydrodynamics in
core-collapse supernova"
http://iopscience.iop.org/1742-6596/125/1/012085/pdf/1742-6596_125_1_012085.pdf

P.S I also tried the variational inequality SNES solver a while back but it
didn't really work in enforcing the constraints.

Thanks,
Mani
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