OpenFOAM computation time

spiers818 · March 30, 2021, 14:18

Hello,
I am running an incompressible, steady state, internal flow model using the k-w turbulence model. I am running the simulation in parallel on 16 cores. In the middle of refining the mesh checking for mesh independence I noticed the run times seemed to be linearly increasing with the number of elements. This seems strange to me as the NS is a non-linear equation I assumed the run time would increase in an exponential manner as the number of elements increase. Can anyone inform me as to why this is?

geth03 · March 31, 2021, 02:39

what makes the NS non-linear is divergence(uu).
in openfoam this term is linearized -> divergence(u_old u_new),
while u_old is the velocity that ensures mass conservation from the old timestep, u_new is the velocity for the new timestep.
this way velocity transports itself.

for more information i suggest reading Jasak's dissertation.

spiers818 · March 31, 2021, 11:39

Hey geth03,
Thanks for the information that is very helpful in understanding this situation.

chegdan · March 31, 2021, 17:16

Just to add to geth03's answer, we aren't actually solving the linearized integral-differential equation directly. We are solving an implicit linear algebra problem that is linear itself

Ax=b

with A being the coefficient matrix (weighting values from the mesh and actual PDE), x being the implicit variable (like temperature or velocity), and b our explicit components. You're seeing the linear scaling because the problem size is growing linearly. Now, this has its limits since as problems grow, there are components in this process that become really difficult to scale linearly or maybe the Ax=b system is too large (or small) for our given number of processors and RAM. If you're interested in Ax=b math, Yousef Saad has a great set of books . His book helped me get started writing the CUDA solvers in OpenFOAM years ago.

March 30, 2021, 14:18	OpenFOAM computation time	#1
spiers818 New Member Chris Join Date: Mar 2021 Posts: 2 Rep Power: 0	Hello, I am running an incompressible, steady state, internal flow model using the k-w turbulence model. I am running the simulation in parallel on 16 cores. In the middle of refining the mesh checking for mesh independence I noticed the run times seemed to be linearly increasing with the number of elements. This seems strange to me as the NS is a non-linear equation I assumed the run time would increase in an exponential manner as the number of elements increase. Can anyone inform me as to why this is?

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March 31, 2021, 02:39		#2
geth03 Senior Member Join Date: Dec 2019 Location: Cologne, Germany Posts: 355 Rep Power: 8	what makes the NS non-linear is divergence(uu). in openfoam this term is linearized -> divergence(u_old u_new), while u_old is the velocity that ensures mass conservation from the old timestep, u_new is the velocity for the new timestep. this way velocity transports itself. for more information i suggest reading Jasak's dissertation.

March 31, 2021, 11:39		#3
spiers818 New Member Chris Join Date: Mar 2021 Posts: 2 Rep Power: 0	Hey geth03, Thanks for the information that is very helpful in understanding this situation.

March 31, 2021, 17:16		#4
chegdan Senior Member Daniel P. Combest Join Date: Mar 2009 Location: St. Louis, USA Posts: 621 Rep Power: 0	Just to add to geth03's answer, we aren't actually solving the linearized integral-differential equation directly. We are solving an implicit linear algebra problem that is linear itself Ax=b with A being the coefficient matrix (weighting values from the mesh and actual PDE), x being the implicit variable (like temperature or velocity), and b our explicit components. You're seeing the linear scaling because the problem size is growing linearly. Now, this has its limits since as problems grow, there are components in this process that become really difficult to scale linearly or maybe the Ax=b system is too large (or small) for our given number of processors and RAM. If you're interested in Ax=b math, Yousef Saad has a great set of books . His book helped me get started writing the CUDA solvers in OpenFOAM years ago.