Instability and stability of numerical approximations to discrete velocity models of the Boltzmann equation
Document Type
Article
Publication Date
1-1-1996
Abstract
We study a standard, explicit finite difference approximation of the 2-D Broadwell model and construct a numerical solution with the sum-norm growing in time faster than any polynomial. Our construction is based on a structure of a self-similar fractal! We also obtain global existence, long-time behavior and numerical stability results of a large class of multidimensional discrete velocity models of the Boltzmann equation. We assume certain restrictions on the size of the support and the sup-norm of the initial data. Our results are obtained by examining the time evolution of sets on which the solutions are supported.
Publication Title
Quarterly of Applied Mathematics
Recommended Citation
Peszek, R.
(1996).
Instability and stability of numerical approximations to discrete velocity models of the Boltzmann equation.
Quarterly of Applied Mathematics,
54(4), 777-791.
http://doi.org/10.1090/qam/1417239
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/9754
