AnalyticQuantities_SimpleFluid.py

import math
 
def kineticContributionsToSRDKinematicShearViscosity(
                                    meanParticleCountPerCell, kT, m,
                                    mpcTimestep, srdAngle):
    M = meanParticleCountPerCell
 
    factor1 = kT * mpcTimestep / (2 * m)
    denominator1 = M - 1 + math.exp(-M)
    denominator2 = 2 - math.cos(srdAngle) - math.cos(2 * srdAngle)
    factor2 = 5 * M / (denominator1 * denominator2) - 1
 
    return factor1 * factor2;
 
def collisionalContributionsToSRDKinematicShearViscosity(
        linearCellSize, meanParticleCountPerCell, mpcTimestep, srdAngle):
    """
    Returns the collisional contribution to the kinematic shear viscosity in SRD,
    according to table 1 in
    Gompper, Ihle, Kroll, and Winkler:
    "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids"
    DOI: 10.1007/12_2008_5
 
    @param[in] linearCellSize           The size of a collision cell. This is called "a" in the reference, and is usually 1.
    @param[in] meanParticleCountPerCell The average number of MPC particles per collision cell.
    @param[in] mpcTimestep              The timestep for the MPC streaming step.
    @param[in] srdAngle                 The rotation angle in SRD.
    """
    M = meanParticleCountPerCell
 
    factor1 = linearCellSize * linearCellSize / (6 * 3 * mpcTimestep);
    factor2 = (M - 1 + math.exp(-M)) / M;
    factor3 = 1 - math.cos(srdAngle);
 
    return factor1 * factor2 * factor3;
 
def approximateSelfDiffusionCoefficient(
                                    meanParticleCountPerCell, m,
                                    kT, mpcTimestep, dimensions, srdAngle):
    M = meanParticleCountPerCell
 
    factor1 = kT * mpcTimestep / (2.0 * m)
    term2 = dimensions * M / ((1 - math.cos(srdAngle)) * (M - 1 + math.exp(-M)))
 
    return factor1 * (term2 - 1)