An Efficient Numerical Study for Anisotropic Nonlinear Models of Competitive Swimming Species

Traditional mathematical modeling and computational efforts have primarily focused on isotropic and linear diffusion or convection of living organisms, assuming uniform motion in all directions. However, these traditional models fail to capture the complexities of the real world where competitive interactions among species in nature often involve spatially heterogeneous and anisotropic diffusive behaviors. Another challenging aspect of such modeling involves scenarios in uid dynamics, where species' movements are in uenced by the ow of the medium. Besides the well-posedness of the mathematical model, this paper is also devoted to investigate an efficient and robust combined finite volume-nonconforming finite element scheme for two-species chemotaxis- uid models including all layers of complex geometrical configurations. Moreover, numerous simulations through a developed code, cover the anisotropic dynamics of species in uids which ensures the scheme's applicability to real-world biological problems. Furthermore, the training data generated through this exible generalized numerical method may be enhanced with artificial intelligence techniques to improve the predictive capabilities.