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Predictor-corrector discrete unified gas kinetic scheme for Boltzmann transport models with non-conservative collision operators
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DOI：10.1016/j.jcp.2026.114886.png)
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Abstract
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A general predictor-corrector discrete unified gas kinetic scheme (PRC_DUGKS) is developed to solve Boltzmann transport models with non-conservative collision operators, including both conservative and non-conservative components. Unlike standard DUGKS formulations that rely on auxiliary distribution functions, PRC_DUGKS directly evolves the original distribution function and incorporates a predictor-corrector strategy to consistently couple transport, conservative and non-conservative collision processes. This proposed formulation eliminates the implicitness introduced by the trapezoidal rule in the time integration and overcomes the limitations of standard DUGKS, where macroscopic variables cannot be directly reconstructed from the moments of the auxiliary distribution function in transport problems with non-conservative collision operators. Furthermore, PRC_DUGKS mitigates the drawbacks of Strang-splitting-based DUGKS (SI_DUGKS), which suffers from operator-splitting errors, accuracy degradation, and numerical instabilities in multiscale problems. The proposed PRC_DUGKS is applied to multigroup neutron transport problems with the conservative and non-conservative collision operators, involving fission, inter-group scattering and absorption terms. Numerical results demonstrate that PRC_DUGKS provides excellent agreement with reference solutions, robustly captures steepgradient features, and maintains accuracy across regimes with varying optical thicknesses. In contrast, SI_DUGKS exhibits significant discrepancies in regions with strong absorbers and nonconservative interactions, particularly under coarse time discretization. These results demonstrate the superior accuracy and numerical efficiency of PRC_DUGKS, highlighting its potential for large-scale engineering applications involving multiscale transport and complex collision physics.
Keywords:
Discrete unified gas kinetic scheme
Predictor-corrector method
Non-conservative and conservative collision
operator
Multiscale modeling
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