Multilevel radial basis function surrogates for noise-robust DSMC-CFD coupling

Abstract

Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD) code. However, widespread adoption of these methods is hindered by numerical instabilities caused by statistical noise and difficulties in applying them to complex, arbitrary geometries. To be effective, a hybrid framework must be robust to noise, reliable in not introducing errors to the flow physics, automated, and flexible enough for general spatial domains. Previous iterations of the micro-macro-surrogate-sparse (MMS-Sparse) method successfully addressed the first three requirements using Bayesian surrogate models to provide smooth, constitutive corrections to the CFD. However, they relied on global basis functions, limiting their applicability to relatively simple geometries. In this work, we address the fourth requirement - flexibility - by introducing a set of multilevel radial basis functions (RBFs) to represent the smooth corrections within the MMS-Sparse framework. Unlike global polynomials, multilevel RBFs can resolve broad and fine flow details locally, allowing the method to be applied to complex geometrical systems. We couple this approach with a finite-volume CFD solver (OpenFOAM) and validate it using the rarefied lid-driven cavity flow problem. This serves as a rigorous test case for spatially two-dimensional coupling. Our results demonstrate that this enhanced MMS-Sparse method produces estimates in good agreement with benchmarks while retaining the noise-robust and automated benefits of the Bayesian approach.