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- W4302362783 abstract "We present a variance-reduced method for efficiently solving the Boltzmann equation in all rarefaction regimes. The proposed method is based on the VRDSMC method of Al-Mohssen and Hadjiconstantinou (2010) [50], which exploits the correlation between two DSMC simulations using the same random numbers to significantly reduce the statistical uncertainty associated with moment estimation. This variance-reduction formulation is preferred here because it requires minimal change to the underlying DSMC method and code base. The instability reported in the collision-dominated regime in this previous work is removed via a combination of Kernel Density Estimation, a hierarchy of moment conservation constraints and a Maximum Entropy formulation for minimizing the bias introduced by the stabilization process. The resulting method is referred to as maximum-entropy variance-reduced direct simulation Monte Carlo (ME-VRDSMC). Computational experiments show that the proposed algorithm provides an efficient and accurate method for solving the Boltzmann equation in the low-signal limit. We also show that, similar to VRDSMC, the relative statistical noise of the proposed method is decoupled from the signal magnitude, leading to a substantial speedup compared to DSMC in the small-signal limit." @default.
- W4302362783 created "2022-10-06" @default.
- W4302362783 creator A5063770046 @default.
- W4302362783 creator A5068470073 @default.
- W4302362783 date "2023-01-01" @default.
- W4302362783 modified "2023-10-01" @default.
- W4302362783 title "A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction" @default.
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- W4302362783 doi "https://doi.org/10.1016/j.jcp.2022.111677" @default.
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