COMPUTER-AIDED ANALYSIS OF 1-D COMPRESSIBLE FLOW PROBLEMS IN A LAGRANGIAN PARTICLE DESCRIPTION USING THE ALPHA-METHOD

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. © 1990.