An alternative procedure for simulating one-dimensional transport phenomena with shock waves in a gas

This article employs an alternative procedure to treat a class of non‐linear hyperbolic systems, using a preliminary model to describe pollutants motion in an atmosphere, accounting for the production or destruction of pollutants, described, as a first approximation, by a source term. The mathematical description consists of a non‐linear hyperbolic system of m+2 partial differential equations representing mass and momentum conservation for the multicomponent mixture of air and gases and mass balance equations for the gases. After simplifying assumptions, the resulting one‐dimensional system of m+2 equations is simulated in such a way that the simultaneous problem is treated sequentially: the operator is splitted into a non‐homogeneous (time‐dependent) ordinary part and a homogeneous associated hyperbolic one. This latter is simulated by a Glimm's scheme for evolution in time, employing an approximate Riemann solver for each two consecutive steps. The employed Riemann solver approximates the solution of the associated Riemann problem by piecewise constant functions always satisfying the jump condition—giving rise to an approximation easier to implement with lower computational cost. Comparison with the standard procedure, employing the complete solution of the associated Riemann problem for implementing Glimm's scheme, has shown good agreement. Copyright © 2009 John Wiley & Sons, Ltd.