Efficient parallel method for implicit upwind schemes approximating the Euler equations in gas dynamics

A grid-overlapping parallel method for some three-point implicit schemes has been proposed by Wu and Zou [J. Comput. Phys. 157 (2000) 2]. In this paper we conduct a theoretical analysis of the convergence speed to steady state for this parallel method when multipoint one-sided upwind schemes are used. The theoretical parallel efficiency is found to be near 100% for the totally time-lagging interface treatment. Numerical experiments for compressible flows are conducted to confirm the linear theory. Moreover, numerical experiments will also be demonstrated for schemes which are not completely upwind.