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Re: [ESPResSo-users] unstable solution flow profile

From: Ulf Schiller
Subject: Re: [ESPResSo-users] unstable solution flow profile
Date: Tue, 25 Mar 2014 16:00:23 +0100
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On 03/25/2014 02:09 PM, Wink, Markus wrote:
Dear all,

while doing simulations on the flow profile in a slit structure, I have
found out that the velocity profile as a function of the grid size
becomes unstable. For example, if I choose a width of 50 microns, a
force density of 64000N/m^3 and a dynamic viscosity of 0.000125 kg/(ms),
the LB-nodes near the maximum velocity starts oscillating and the
profile collapses, when the grid size is set to 1. When I start a
simulation using a grid size of 0.5, the solution is stable.

I was wondering, why that is the case. I mean, what is the physical
reason for that and why does it happen near the maximum? I mean, I can
deal with that problem, but I am really curios to know, what the reason
is. Attached you will find the two flow profiles.

Hi Markus,

I think the origin is of numerical nature: I suspect that your (grid scale) Reynolds number is rather high. The accuracy of LB depends on h/\tau indeed, where h is the LB timestep and \tau the relaxation time. Ignoring the discrete correction we have
h/\tau = 1/3*a^2/(h*\nu)
so by reducing the grid size you reduce the grid scale Reynolds number and presumably bring the LB back into the stable regime. Note that h/\tau scales with a^2 while the Mach number scales with 1/a, i.e., reducing the grid size too much will drive you into a different instability (physically related to compressibility).

Hope this helps,

Dr. Ulf D. Schiller                        Building 04.16, Room 3006
Institute of Complex Systems (ICS-2)       Phone:   +49 2461 61-6144
Forschungszentrum J├╝lich, Germany          Fax:     +49 2461 61-3180

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