A unified stochastic particle method with spatiotemporal adaptation for simulating multiscale gas flows

Abstract

Recently, the Unified Stochastic Particle (USP) method has emerged as a promising approach for multiscale particle simulations, tailored specifically for non-equilibrium gas flow scenarios. However, in typical simulations of multiscale flow fields, the time step and grid size of the original USP method remain constrained by the smallest spatiotemporal scale of local flow field, limiting its true multiscale simulation potential. To overcome this critical issue, this work introduces a spatiotemporal adaptive USP method. Initially, we analyze the sources of errors in the traditional single-scale stochastic particle methods under large time steps, which leads to the derivation of the governing equations of USP. Building upon this foundation, we propose principles that dictate the rational time step and grid size for an arbitrary USP simulation. Subsequently, we introduce a spatiotemporal adaptive approach primarily based on the local gradient length, leading to the development of a USP solver endowed with spatiotemporal adaptability. The universality, reliability, and efficiency of the algorithm have been verified through an examination of three cases: two-dimensional flow over a cylinder, three-dimensional flow over a blunted body, and flow over a scaled X38-like model. This work forms an integral component of the development initiative for the general USP solver—SPARTACUS—with relevant source code being open-source in an online repository under the GNU General Public License (GPL).