Computer aided analysis of 1D compressible flow problems in a Lagrangian particle description using the alpha method
Abstract
The alpha method is a simple finite difference method for analyzing onedimensional 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 (Delta t, Delta alpha). The weighted time difference is shown to be equivalent to adding a diffusion term whose coefficient is proportional to the value of (1  alpha). Selecting values of alpha in the range 01 noticeably improves the results as compared with Lax differencing while retaining the ease of coding for which the Lax method is known. The alpha method is shown to be extremely robust by solving a number of problems involving several different boundary conditions.
 Publication:

Computers and Fluids
 Pub Date:
 1990
 Bibcode:
 1990CF.....18...75K
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 One Dimensional Flow;
 Density Distribution;
 Error Analysis;
 Mach Number;
 Pressure Distribution;
 Wave Interaction;
 Fluid Mechanics and Heat Transfer