Force term – Units ?

[Alejandro_Claro]

Hello everyone,rnrnI am trying to simulate the flow of water in 3D channel taking into account the gravity force. I checked how to implement the force term in the poiseuille-forced-2d example. I know that this force term have been implemented form the Gou et al. (2002) paper. rnrnSomeone knows the units of this term? If I used the acceleration of the gravity in earth, could I use 10 m²/s as the magnitude of the gravity acceleration for the vertical component of this term? rnrnPD: Gou et al. (2002) Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E, Vol. 65, 046308.rnrnBest Regards,rnAlejandro

[robin.trunk]

Hi Alejandro,rnrnthe way it is implemented, lattice units are used. In the example for the computation of the force also lattice units are used (getLatticeNu()).rnIf you want to implement gravity, you can do this analogously to the poiseuille-forced-2d example and convert the force in physical units to lattice units byrnconverter.latticeForce(value)rnFor more information have a look at the doxygen:rnhttp://optilb.com/DoxyGen/html/d1/d25/classolb_1_1LBconverter.html#a842f574807fc0592fd9deea0ad272fc0rnrnBest regardsrnRobin

[Alejandro_Claro]

Hi Robin,rnrnThank you for your response. However, I am still confuse about how it is implemented this body force.rnrnIf m** is the length in lattice units and t** is the time in lattice units. Then, according to the line of code for the poiseuille-forced-2d example:rn

Code:

T Ly = converter.numCells(ly);rn std::vector<T> poiseuilleForce(2,T());rn poiseuilleForce[0] = 8.*converter.getLatticeNu()*converter.getLatticeU() / (Ly*Ly);

rnThe poiseuilleForce x-component vector has acceleration lattice units (m**/(s**)²). In the poiseuille-forced-2d example the characteristics density and length are both unity. Thus, the “”mass”” in lattice units [CharRho * DeltaX³] is equal to 1. This is the reason why it is not wrote the “”mass”” in lattice units?rnrnThe body force F = rho*g [kg/m³ * m/s²] defined in Ghou et al. (2002) has not the units of N [kg * m/s²]. Thus, LBconverter.latticeForce(value) should not be used because the force in the physical system (value) will be dimensionless by LBconverter.physForce() which has N physical units. It is that right? rnrnIn the case of a incompressible and isothermal problem, the body force term g in the Navier-Stokes equations have [m/s²] physical units. This body force term in the dimensionless Navier-Stokes equations is:rn

Code:

g_d = 1/Fr² // Fr is the Froude number

rnTo pass from dimensionless to lattice units I use the same procedure presented in Latt (2008).rn

g_d = dx/dt² * g_lbrng_lb = dt²/dx * g_drng_lb = dt²/dx * (1/Fr²)

rnI would like to know if it is correct to insert this gravity acceleration in lattice units [g_lb] in the force vector ? rnrnPD: Ghou et al. (2002) Discrete lattice effects on the forcing term in the lattice Boltzmann method.rnLatt (2008) Choice of units in lattice Boltzmann simulations.rnrnBest regards,rnrnAlejandro

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