A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

A Fourier spectral methods for homogeneous Botzmann equations

PARESCHI, Lorenzo;
1996

Abstract

A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.
1996
Pareschi, Lorenzo; B., Perthame
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1397057
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