Approximation of the Solution to a System Modeling Heatless Adsorption of Gases

We present both time and space-time explicit approximation schemes for a system of first-order nonlinear transport PDEs used as a model in chemical engineering. For the time discretization, using a splitting, we introduce an intermediate spatial regularization step to obtain some bounded variation (BV) estimates for the approximate solutions (with BV initial data), and we get an O(∆t1/2) L convergence rate. With respect to the fully discrete finite volume scheme, we show that it is possible to get such estimates without any regularization step because of the dissipative effect of the upwind scheme used to treat the transport part of the equations. This scheme is convergent.