Skip to content

Re: ComputeStress Function – Error ?


Hi Mathias,rnrnThe ComputeStress seems to give the second-order moment of the non-equilibrium distribution fi(1). The second-order moment of the distribution function is Sigma(Ci_A*Ci_B*[fi – fi(0)]). Ci is the discrete velocity; fi and fi(0) are the actual and the the equilibrium distribution functions in the lattice, respectively.rnrnSupposing that BGK collision model is used with a rectangular method for the collision operator. Then, the kinematic shear viscosity is

nu = (tau – 0.5)*pow(Cs,2)

Where Cs is the velocity of the sound in the lattice system and tau is the relaxation time. The pressure is defined by

P = pow(Cs,2)*rho

The second-order moment of the equilibrium distribution fi(0) is rn

rnSecond_Order_Moment_fi0 = rho*u_A*u_B + P* KroneckerDelta(A,B);rnSecond_Order_Moment_fi0 = rho*u_A*u_B + (pow(Cs,2)*rho)* KroneckerDelta(A,B);rn

rnrnSo, the pressure is already is taken by the second right-side term of the previous expression, or I am wrong ? Thus, I do not understand why the extra term -1.*pow(Cs,2) is added to the previous expression? rnrnIn the user guide is indicated that the Smagorinsky model is based in the paper Nathen et al. (2013) An extension of the Lattice Boltzmann Method for simulating turbulent flows around rotating geometries of arbitrary shape. Unfortunately, I do not have access rights to read this document. The pressure term in this paper is obtained differently from the previous “”explanation”” ?rnrnBest Regards,rnrnAlejandro