Adaptive moving mesh upwind scheme for the two-species chemotaxis model

Chemotaxis systems are used to model the propagation, aggregation and pattern formation of bacteria/cells in response to an external stimulus, usually a chemical one. A common property of all chemotaxis systems is their ability to model a concentration phenomenon—rapid growth of the cell density in small neighborhoods of concentration points/curves. More precisely, the solution may develop singular, spiky structures, or even blow up in finite time. Therefore, the development of accurate and computationally efficient numerical methods for the chemotaxis models is a challenging task.