Spectral convergence of the stochastic galerkin approximation to the boltzmann equation with multiple scales and large random perturbation in the collision kernel
- Vienna Univ. of Technology (Austria). Inst. for Analysis and Scientific Computing; DOE/OSTI
- Shanghai Jiao Tong Univ. (China). Inst. of Natural Sciences, MOE-LSC and SHL-MAC
- Univ. of Texas, Austin, TX (United States). Inst. for Computational Engineering and Sciences
In a 2018 article, spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation with random inputs in the initial data and collision kernel for hard potentials and Maxwellian molecules under Grad's angular cutoff were established using the hypocoercive properties of the collisional kinetic model. One assumption for the random perturbation of the collision kernel is that the perturbation is in the order of the Knudsen number, which can be very small in the fluid dynamical regime. In this article, we remove this smallness assumption, and establish the same results but now for random perturbations of the collision kernel that can be of order one. The new analysis relies on the establishment of a spectral gap for the numerical collision operator.
- Research Organization:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- SC0016283
- OSTI ID:
- 1612472
- Journal Information:
- Kinetic & Related Models, Journal Name: Kinetic & Related Models Journal Issue: 4 Vol. 12; ISSN 1937-5077
- Publisher:
- American Institute of Mathematical Sciences
- Country of Publication:
- United States
- Language:
- English
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