Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
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Sergey V. Rogasinsky
Abstract
The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.
Funding: The work was supported by the Russian Foundation for Basic Research (project No. 18-01-00356 a), and the Program of fundamental research of the Presidium of RAS I.33II.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
Artikel in diesem Heft
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
