Płatkowski, T.; Waluś, W. An acceleration procedure for discrete velocity approximation of the Boltzmann collision operator. (English) Zbl 0949.65141 Comput. Math. Appl. 39, No. 5-6, 151-163 (2000). Summary: We investigate a method of realization of the discrete velocity approximation of the Boltzmann collision operator studied by A. Palczewski, J. Schneider and A. V. Bobylev [SIAM J. Numer. Anal. 34, No. 5, 1865-1883 (1997; Zbl 0895.76083)]. For this realization, we propose an acceleration procedure, which reduces the computational complexity of the method. The efficiency of the acceleration procedure is demonstrated through a set of numerical tests, which include space homogeneous relaxation problems and space nonhomogeneous problems of shock wave formation. Cited in 4 Documents MSC: 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 82C40 Kinetic theory of gases in time-dependent statistical mechanics 65Y20 Complexity and performance of numerical algorithms Keywords:Boltzmann equation; numerical algorithms; discrete velocity approximation; kinetic theory of rarefied gases; Boltzmann collision operator; computational complexity; numerical tests; shock wave formation Citations:Zbl 0895.76083 PDFBibTeX XMLCite \textit{T. Płatkowski} and \textit{W. Waluś}, Comput. Math. Appl. 39, No. 5--6, 151--163 (2000; Zbl 0949.65141) Full Text: DOI References: [1] Cercignani, C., Theory and Applications of the Boltzmann Equation (1988), Springer-Verlag [2] Truesdell, C.; Muncaster, R., Fundamentals of Maxwell’s Kinetic Theory of a Simple Monoatomic Gas (1980), Academic Press [3] Nordsieck, A.; Hicks, B. L., Monte Carlo evaluation of the Boltzmann collision integral, (Brundin, C. L., Proc. \(5^{th}\) Intern. 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