Abstract
The Direct Simulation Monte Carlo (DSMC) scheme of Nanbu is considered for the solution of the Boltzmann equation in a simplified case. It is interpreted as a one-step method using particles combined with numerical quadratures after each step. A modified scheme in which the particles are ordered after each step is proposed. It is called the Low Discrepancy (LD) method. The error of the LD method is defined as the discrepancy of the set of particles relative to the exact solution. This error is estimated by means of other discrepancies, namely those of the sequences which perform the quadratures. The replacement of pseudo-random numbers used in the quadratures by uniformly distributed sequences is consequently suggested. Numerical comparisons are given between the DSMC scheme and the LD method that repeatedly uses the Hammersley sequence in the quadratures (LDH method).
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