The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods and discrete velocity methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and, in particular, for the spectral method spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.
Fast algorithms for computing the Boltzmann collision operator
PARESCHI, Lorenzo
2006
Abstract
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods and discrete velocity methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and, in particular, for the spectral method spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.