- Katz, Ira M. and Shaughnessy, Edward J., Computer aided analysis of 1-D compressible flow problems in a Lagrangian particle description using the α method,
Computers & Fluids, vol. 18 no. 1
pp. 75 - 101 [0045-7930(90)90004-H] .
(last updated on 2007/04/06)
The α method is a simple finite difference method for analyzing one-dimensional compressible flow problems in the Lagrangian particle description which is easy to code for a variety of applications in science and engineering. The method employs a weighted average of Euler and Lax time differencing to construct a conservative finite difference algorithm which performs well on a variety of problems with an error which is of order (δt, δa). The weighed time difference is shown to be equivalent to adding a diffusion term whose coefficient is proportional to the value of (1 - α). Selecting values of α in the range 0 <= α <= 1 noticeably improves the results as compared with Lax differencing while retaining the ease of coding for which the Lax method is known. The α method is shown to be extremely robust by solving a number of problems involving the application of several different boundary conditions.
Computer Aided Analysis;Mathematical Techniques--Finite Difference Method;Fluid Dynamics;Gas Dynamics;Pistons;