Multiscale simulation of heat transfer in a rarefied gas

We present a new hybrid method for dilute gas flows that couples a continuum-fluid description to the direct simulation Monte Carlo (DSMC) technique. Instead of using a domain-decomposition framework, we adopt a heterogeneous approach with micro resolution that can capture non-equilibrium or non-continuum fluid behaviour both close to bounding walls and in the bulk. A continuum-fluid model is applied across the entire domain, while DSMC is applied in spatially-distributed micro regions. Using a field-wise coupling approach, each micro element provides a local correction to a continuum sub-region, the dimensions of which are identical to the micro element itself. Interpolating this local correction between the micro elements then produces a correction that can be applied over the entire continuum domain. Key advantages of this method include its suitability for flow problems with varying degrees of scale separation, and that the location of the micro elements is not restricted to the nodes of the computational mesh. Also, the size of the micro elements adapts dynamically with the local molecular mean free path. We demonstrate the method on heat transfer problems in dilute gas flows, where the coupling is performed through the computed heat fluxes. Our test case is micro Fourier flow over a range of rarefaction and temperature conditions: this case is simple enough to enable validation against a pure DSMC simulation, and our results show that the hybrid method can deal with both missing boundary and constitutive information.