[TTY]

Hi there,

I've written a program in C which solves the complete, time-dependent 2-d Navier-Stokes incompressible equations and equations of motion of discs in liquid in order to investigate sedimentation without any external forces. The number of points in the grid: 512x512. The ratio of the particle density to the liquid density is 1.1 and the Reynolds number is small, about 0.1. So the liquid disturbance due to sedimentation is rather small.

My program is doing calculations very slowly for such small parameters since the particles movement is very slow, the disturbance of liquid is low, and the time-step is small too.

I'm using an ordinary laptop for my calculations. How long does it usually take to complete such calculations (for these small parameters and the full 2-d N-S eqs.) up to the full sedimentation, if I would use the fastest code (or some package, etc.) which can exist in the world nowadays?

[FMDenaro]

Originally Posted by TTY

Hi there,

I've written a program in C which solves the complete, time-dependent 2-d Navier-Stokes incompressible equations and equations of motion of discs in liquid in order to investigate sedimentation without any external forces. The number of points in the grid: 512x512. The ratio of the particle density to the liquid density is 1.1 and the Reynolds number is small, about 0.1. So the liquid disturbance due to sedimentation is rather small.

My program is doing calculations very slowly for such small parameters since the particles movement is very slow, the disturbance of liquid is low, and the time-step is small too.

I'm using an ordinary laptop for my calculations. How long does it usually take to complete such calculations (for these small parameters and the full 2-d N-S eqs.) up to the full sedimentation, if I would use the fastest code (or some package, etc.) which can exist in the world nowadays?

1) in your case the dt is constrained mainly by the diffusive fluxes, are you using an implicit integration?
2) The most part of the computational step will be in the elliptic solver, what are you using?

[TTY]

Originally Posted by FMDenaro

1) in your case the dt is constrained mainly by the diffusive fluxes, are you using an implicit integration?
2) The most part of the computational step will be in the elliptic solver, what are you using?

1) I used the implicit method, and for my parameters it works only a little bit faster than the explicit one.

2) I use FFT, fast solver for the Poisson equation.

But how long does the program usually last for such problems and for my parameters?

[FMDenaro]

Originally Posted by TTY

1) I used the implicit method, and for my parameters it works only a little bit faster than the explicit one.

2) I use FFT, fast solver for the Poisson equation.

But how long does the program usually last for such problems and for my parameters?

Implicit method leads to an algebric system, how do you solve? In any case I don't know what you expect for a fast code, your case requires a small time-step but:

1) at this low Re number I suspect you have a laminar steady flow, it is correct?
2) the motion of particles is resolved after the steady state is achieved or you need to solve it during the transient stage?

[TTY]

Originally Posted by FMDenaro

Implicit method leads to an algebric system, how do you solve? In any case I don't know what you expect for a fast code, your case requires a small time-step but:

1) at this low Re number I suspect you have a laminar steady flow, it is correct?
2) the motion of particles is resolved after the steady state is achieved or you need to solve it during the transient stage?

1) Yeah, but I don't want to exclude the non-linear term in the Navier-Stokes equation.
2) I'm interested in the investigation of all time scales.

[FMDenaro]

even considering the non-linear terms I suppose your case has a steady solution.... thus, if you are considering a one-way particle tracking, you can solve for the steady state and the integrate for the particles.
But you should clarify if you are interested in studyng also the transient..