In this paper we show that the use of spectral-Galerkin methods for the approximation of the Boltzmann equation in the velocity space permits to obtain spectrally accurate numerical solutions at a reduced computational cost. We prove that the spectral algorithm preserves the total mass and approximates with innite-order accuracy momentum and energy. Consistency of the method is also proved and a stability result for a smoothed positive scheme is given. We demonstrate that the Fourier coeÆcients associated to the collision kernel of the equation have a very simple structure and in some cases can be computed explicitly. Numerical examples for homogeneous test problems in two and three dimensions conrm the advantages of the method.
Numerical solution of the Boltzmann equation I: Spectrally accurate approximation of the collision operator
PARESCHI, Lorenzo;
2000
Abstract
In this paper we show that the use of spectral-Galerkin methods for the approximation of the Boltzmann equation in the velocity space permits to obtain spectrally accurate numerical solutions at a reduced computational cost. We prove that the spectral algorithm preserves the total mass and approximates with innite-order accuracy momentum and energy. Consistency of the method is also proved and a stability result for a smoothed positive scheme is given. We demonstrate that the Fourier coeÆcients associated to the collision kernel of the equation have a very simple structure and in some cases can be computed explicitly. Numerical examples for homogeneous test problems in two and three dimensions conrm the advantages of the method.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.