Computationally Efficient Cell-Level Thermostating for SRD

The MFC-AT algorithm discussed in Sect 2.2 provides a very efficient particle-level thermostating of the system. However, it is considerably slower than the original SRD algorithm, and there are simations in which the additional fieedom offered by the choice of SRD collision angle can be useful. 

Thermostating is required in any non-equilibrium MFC simulation, where there is viscous heating. A basic requirement of any thermostat is that it does not violate local momentum conservation, smear out local flow profiles, or distort the velocity distribution too much. When there is homogeneous heating, the simplest way to maintain a constant temperature is to just rescale velocity components by a scale factor 5, = Sva, which adjusts the total kinetic energy to the desired value. 

This can be done with just a single global scale factor, or a local factor which is different in every cell. For a known macroscopic flow profile, u, like in shear flow, the relative velocities v - u can be rescaled. This is known as a profile-unbiased thermostat however, it has been shown to have deficiencies in molecular dynamics simulations [41], 

Here we describe an alternative thermostat which exactly conserves momentum in every cell and is easily incorporated into the MFC collision step. It was originally developed by Heyes for constant-temperature molecular dynamics simulations however, the original algorithm described in [42] violates detailed balance. The thermostat consists of the following procedure which is performed independently in every collision cell as part of the coUision step  

Randomly select a real number i/r e [ 1,1 -f- c], where c is a small number between 0.05 and 0.3 which determines the strength of the thermostat. 

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