Changing resolution

[iJokerify]

Hi all,

I’m trying to change the resolution in cylinder3d example from N to N*2:
from

UnitConverterFromResolutionAndRelaxationTime<T, DESCRIPTOR> const converter(
    int {N},              // resolution
    (T)   0.53,           // latticeRelaxationTime
    (T)   0.1,            // charPhysLength
    (T)   0.2,            // charPhysVelocity
    (T)   0.2*2.*0.05/Re, // physViscosity
    (T)   1.              // physDensity
  );

to

UnitConverterFromResolutionAndRelaxationTime<T, DESCRIPTOR> const converter(
    int {N*2},            // resolution
    (T)   0.53,           // latticeRelaxationTime
    (T)   0.1,            // charPhysLength
    (T)   0.2,            // charPhysVelocity
    (T)   0.2*2.*0.05/Re, // physViscosity
    (T)   1.              // physDensity
  );

The converter’s output changing
from

[UnitConverter] ----------------- UnitConverter information -----------------
[UnitConverter] -- Parameters:
[UnitConverter] Resolution:                       N=              10
[UnitConverter] Lattice velocity:                 latticeU=       0.02
[UnitConverter] Lattice relaxation frequency:     omega=          1.88679
[UnitConverter] Lattice relaxation time:          tau=            0.53
[UnitConverter] Characteristical length(m):       charL=          0.1
[UnitConverter] Characteristical speed(m/s):      charU=          0.2
[UnitConverter] Phys. kinematic viscosity(m^2/s): charNu=         0.001
[UnitConverter] Phys. density(kg/m^d):            charRho=        1
[UnitConverter] Characteristical pressure(N/m^2): charPressure=   0
[UnitConverter] Mach number:                      machNumber=     0.034641
[UnitConverter] Reynolds number:                  reynoldsNumber= 20
[UnitConverter] Knudsen number:                   knudsenNumber=  0.00173205
[UnitConverter] 
[UnitConverter] -- Conversion factors:
[UnitConverter] Voxel length(m):                  physDeltaX=     0.01
[UnitConverter] Time step(s):                     physDeltaT=     0.001
[UnitConverter] Velocity factor(m/s):             physVelocity=   10
[UnitConverter] Density factor(kg/m^3):           physDensity=    1
[UnitConverter] Mass factor(kg):                  physMass=       1e-06
[UnitConverter] Viscosity factor(m^2/s):          physViscosity=  0.1
[UnitConverter] Force factor(N):                  physForce=      0.01
[UnitConverter] Pressure factor(N/m^2):           physPressure=   100
[UnitConverter] -------------------------------------------------------------

to

[UnitConverter] ----------------- UnitConverter information -----------------
[UnitConverter] -- Parameters:
[UnitConverter] Resolution:                       N=              20
[UnitConverter] Lattice velocity:                 latticeU=       0.01
[UnitConverter] Lattice relaxation frequency:     omega=          1.88679
[UnitConverter] Lattice relaxation time:          tau=            0.53
[UnitConverter] Characteristical length(m):       charL=          0.1
[UnitConverter] Characteristical speed(m/s):      charU=          0.2
[UnitConverter] Phys. kinematic viscosity(m^2/s): charNu=         0.001
[UnitConverter] Phys. density(kg/m^d):            charRho=        1
[UnitConverter] Characteristical pressure(N/m^2): charPressure=   0
[UnitConverter] Mach number:                      machNumber=     0.0173205
[UnitConverter] Reynolds number:                  reynoldsNumber= 20
[UnitConverter] Knudsen number:                   knudsenNumber=  0.000866025
[UnitConverter] 
[UnitConverter] -- Conversion factors:
[UnitConverter] Voxel length(m):                  physDeltaX=     0.005
[UnitConverter] Time step(s):                     physDeltaT=     0.00025
[UnitConverter] Velocity factor(m/s):             physVelocity=   20
[UnitConverter] Density factor(kg/m^3):           physDensity=    1
[UnitConverter] Mass factor(kg):                  physMass=       1.25e-07
[UnitConverter] Viscosity factor(m^2/s):          physViscosity=  0.1
[UnitConverter] Force factor(N):                  physForce=      0.01
[UnitConverter] Pressure factor(N/m^2):           physPressure=   400
[UnitConverter] -------------------------------------------------------------

The Mach and Knudsen numbers and several differ characteristics is changing. The flow output images (every 0.1 sec) of these two simulations are very different like if the flow velocity rate has become greater. How to change resolution without change in flow ?

Gratefully,
Sergey

[mgaedtke]

Hi Sergey,

using a constant relaxation time while changing the resolution results in changing the lattice velocity as well. These parameters are not independent. However, the Reynolds number is 20 for both cases. So, you should see similar simulation results for both cases. Keep in mind that changing the discretization will also change corresponding discretization errors.

For a good write up of the dimensionalization of the lattice boltzmann equation, have a look in the book by Krüger et al., chapter 7 (https://www.springer.com/de/book/9783319446479).

Best,
Max

[iJokerify]

Hi Max,

thanks for your reply. I should deal with the parameters a bit.

Grateful,
Sergey

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