Numerical Modeling of Transport Barrier Formation

In diverse media the characteristics of mass and heat transfer may undergo spontaneous and abrupt changes in time and space. This can lead to the formation of regions with strongly reduced transport, the so called transport barriers (TB). Interfaces between regions with qualitatively and quantitatively different transport impose severe requirements to the methods for solving of transport equations. Thus assumptions made in standard methods about the solution behavior by representing its derivatives fail in points where the transport changes abruptly. A numerical approach operating reliably under such conditions is proposed. It is based on the introduction of a new dependent variable related to the volume integrated time derivative of the original one. The resulting differential equation is solved by conjugating exact analytical solutions valid in the vicinity of grid knots. As an example the heat transport with a heat conductivity decreasing abruptly if the temperature e-folding length exceeds a critical level is considered. The TB generation both by the heating exceeding the critical level and under subcritical conditions by radiation losses non-linearly dependent on the temperature is simulated.