ON PARTICLE GRID INTERPOLATION AND CALCULATING CHEMISTRY IN PARTICLE-IN-CELL METHODS

A generalized Fisher’s equation, which models chemically reacting fluid flow and for which there is an analytic solution for a one-dimensional premixed flame, is solved numerically using three particle-in-cell (PIC) methods and a finite-difference method that is second-order accurate in space. Two of the PIC methods introduce new particle-grid interpolation schemes that use mass matrix formulations. Through comparisons with the analytic solution and through truncation error analyses, it is shown that the two new interpolation schemes are superior to the standard PIC method and are as accurate as the finite-difference method when the fluid velocity is comparable to the flame velocity. All three PIC methods give superior results when the fluid velocity is greater than the flame velocity. Solving chemical rate equations on the grid instead of on each particle yields significant increases in computational efficiency with no significant increases in numerical error. © 1993 by Academic Press, Inc.