Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
Abstract
Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically
O(
N
2d+1
)
where
d
is the dimension of the velocity space. In this paper, following the ideas introduced in [27,28], we derive fast summation techniques for the evaluation of discrete-velocity schemes which permits to reduce the computational cost from
O(
N
2d+1
)
to
O(
N
¯
d
N
d
log
2
N)
,
N
¯
<<N
, with almost no loss of accuracy.