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Robustly hyperbolic high-order moment-closures for multidimensional gases
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DOI：10.1016/j.jcp.2026.115026.png)
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Abstract
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Moment closures offer many advantages over traditional methods when it comes to the prediction of transition-regime gas flows. Recently, much work has been done developing robust, globally hyperbolic moment closures for a one-dimensional gas with an arbitrary number of moments. However, extending these to a realistic three-dimensional gas is often difficult. This work demonstrates a technique to extend one-dimensional moment closures to three-dimensional velocity space, allowing for the extension of these new arbitrary-order moment methods to be used in realistic settings. Two 20-moment closures are presented, the first showing the extension of the new 4-moment closure that is robustly hyperbolic and translationally invariant. However it was found that this closure does not preserve rotational symmetries. A second 20-moment closure with improved rotational properties is then presented. Numerical solutions to one-dimensional Riemann problems for Sod shock tubes, simulating a real three-dimensional gas, are examined in the continuum, transition, and free-molecular regimes. Next, a fully multidimensional discontinuous bubble problem is studied, to demonstrate differences in rotational properties over the same three regimes. Finally, high-Mach-number stationary shocks are presented, investigating the resulting shock structure of the models as a realistic sample problem. A 35-moment closure is also presented in the appendix, demonstrating the techniques ability to be extended to arbitrarily-high order moment closures.
Keywords:
Kinetic theory
Moment closures
Hyperbolic PDEs
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