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Hierarchical Micro-Macro Acceleration for Moment Models of Kinetic Equations

by   Julian Koellermeier, et al.

Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using more accurate microscopic models is often expensive. In this paper, we introduce a hierarchical micro-macro acceleration based on moment models that combines the speed of macroscopic models and the accuracy of microscopic models. The hierarchical micro-macro acceleration is based on a flexible four step procedure including a micro step, restriction step, macro step, and matching step. We derive several new micro-macro methods from that and compare to existing methods. In 1D and 2D test cases, the new methods achieve high accuracy and a large speedup.


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