Bulk viscosity of multiparticle collision dynamics fluids

We determine the viscosity parameters of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale hydrodynamic simulation method for fluids. We perform analytical calculations and verify our results by simulations. The stochastic rotation dynamics and the Andersen thermostat variant of MPC are considered, both with and without angular momentum conservation. As an important result, we find a nonzero bulk viscosity for every MPC version. The explicit calculation shows that the bulk viscosity is determined solely by the collisional interactions of MPC.

Figure 1

Shear viscosity $\eta$ for a SRD+a fluid. The open symbols denote simulation results for the MPC parameters $\langle N_c\rangle =10,\alpha ={130}^{\circ }$, the shear rate $\dot{\gamma }=0.01\sqrt{k_{B}T/\left(m{a}^2\right)}$, and the size of the cubic simulation box $L=40a$. The solid line represents the theoretical result provided in Ref. [65]. The measured values are also listed in Table 2.

Figure 2

Bulk viscosities of $\mathrm{MPC}\pm \mathrm{a}$ variants for various collision steps $h$. Circles (red) and diamonds (blue) correspond to SRD−a and SRD+a fluids, respectively, while the squares (green) and triangles (magenta) correspond to AT−a and AT+a fluids. The simulation parameters are $\langle N_c\rangle =10,\alpha ={130}^{\circ }$, and $L=10a$ for SRD, and $\langle N_c\rangle =5$ for AT. The black lines represent the theoretical expectation ${\eta }^V={\eta }^c/3$, where ${\eta }^c$ is the collisional viscosity of MPC−a [Eq. (30)]. The top solid and bottom dashed line correspond to SRD and AT, respectively.

Figure 3

Longitudinal velocity autocorrelation function for $k=2\pi /L$ and the length $L=40a$ of a cubic box. The red and blue lines correspond to SRD+a with $\langle N_c\rangle =10,\alpha ={130}^{\circ }$, and $h/\sqrt{m{a}^2/\left(k_{B}T\right)}=0.01$; the green and black lines correspond to AT+a with $\langle N_c\rangle =10$ and $h/\sqrt{m{a}^2/\left(k_{B}T\right)}=0.05$. Dashed lines represent simulation results. The solid lines represent the theoretical expression Eq. (20) with $\tilde{\nu }=(4\eta /3+{\eta }^V)/{\rho }_0$, while for the dotted lines the viscosity $\tilde{\nu }=(4\eta /3)/{\rho }_0$ without bulk contribution is used.