1. Hierarchical micro-macro acceleration for moment models of kinetic equations
- Author
-
Julian Koellermeier and Hannes Vandecasteele
- Subjects
Technology ,Physics and Astronomy (miscellaneous) ,2) ,SCHEMES ,Stiffness ,Boltzmann equation ,FOS: Mathematics ,(1 ,Mathematics - Numerical Analysis ,Moment model ,( f ,Numerical Analysis ,Science & Technology ,Physics ,Applied Mathematics ,Kinetic equation ,f M ) ,ORDER ,Numerical Analysis (math.NA) ,Micro -macro decomposition ,Computer Science Applications ,Physics, Mathematical ,PROJECTIVE INTEGRATION ,Computational Mathematics ,Modeling and Simulation ,Physical Sciences ,Computer Science ,SIMULATION ,Computer Science, Interdisciplinary Applications ,SYSTEM - Abstract
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.
- Published
- 2023