Formulation and Stability Analysis of Rapidly Convergent Iteration Schemes for the 2‐D Linearized BGK Equation

Various H_N rapidly convergent schemes are proposed to speed up the slow convergence of the iterative solution of 2‐D linearized Bhatnagar‐Gross‐Krook (BGK) kinetic equation containing up to the first moments of the distribution function. The formulation of the 2‐D H_N acceleration schemes is provided in a generalized manner, followed by a formal 2‐D Fourier‐mode stability analysis to determine the most efficient H_N approach. The H₀ method is the most efficient when the kinetic equation contains only the zeroth moment of the distribution function, while when it contains the zeroth and the first moments the most efficient approach is the H₁. Although the analysis and the conclusions are restricted to the continuous form of the equations, they are indicative for the associated discrete equations.

Keywords:

• Kinetic
• Discrete velocities
• Iteration
• Acceleration

Acknowledgments

The authors take this opportunity to thank Professor E. W. Larsen for several helpful discussions and comments regarding this (and other) work. Partial support by the Association EURATOM—Hellenic Republic (Controlled Thermonuclear Fusion program) and the Greek Ministry of Education (Pythagoras program) is gratefully acknowledged.