Title
Acceleration Schemes of the Discrete Velocity Method: Gaseous Flows in Rectangular Microchannels
Abstract
The convergence rate of the discrete velocity method (DVM), which has been applied extensively in the area of rarefied gas dynamics, is studied via a Fourier stability analysis. The spectral radius of the continuum form of the iteration map is found to be equal to one, which justifies the slow convergence rate of the method. Next the efficiency of the DVM is improved by introducing various acceleration schemes. The new synthetic-type schemes speed up significantly the iterative convergence rate. The spectral radius of the acceleration schemes is also studied and the so-called H1 acceleration method is found to be the optimum one. Finally, the two-dimensional flow problem of a gas through a rectangular microchannel is solved using the new fast iterative DVM. The number of required iterations and the overall computational time are significantly reduced, providing experimental evidence of the analytic formulation. The whole approach is demonstrated using the BGK and S kinetic models.
Year
DOI
Venue
2003
10.1137/S1064827502406506
SIAM Journal on Scientific Computing
Keywords
Field
DocType
iterative methods,acceleration schemes,rarefied gas flows
Mathematical optimization,Spectral radius,Fourier analysis,Iterative method,Mathematical analysis,Acceleration,Rate of convergence,Numerical analysis,Two-dimensional flow,Mathematics,Numerical stability
Journal
Volume
Issue
ISSN
25
2
1064-8275
Citations 
PageRank 
References 
7
2.03
0
Authors
2
Name
Order
Citations
PageRank
Dimitris Valougeorgis172.03
Stergios Naris272.03