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Center for Nonlinear Studies |
We formulate a numerical method for evaluating the Boltzmann collision integral in O(MN) operations, where N is the number of discrete velocity points in the three dimensional velocity space and M < N. We use the nodal-discontinuous Galerkin method to discretize collision operator on uniform grids in the velocity variable as the base for the algorithm. We derive the bilinear convolution form of the Galerkin projection of the collision operator. Efficiency of the method is achieved by applying the SVD compression to the discrete collision kernel and the kernel density estimation of the velocity distribution as a sum of Maxwellian streams using a stochastic algorithm that is based on randomization. Accuracy of the method is demonstrated on the relaxation of the solutions to the spatially homogeneous problem.
Host: Luis Chacon