Kinetic-fluid derivation and mathematical analysis of a nonlocal cross-diffusion–fluid system.

• Derivation of a new nonlocal kinetic-fluid model by use the micro-macro decomposition method. • Proof of the existence of weak solutions for the proposed system. • Performance of the proposed schemes during the transition from the kinetic regime to the macroscopic regime. • Demonstration of the phenomenon of pattern formation. In this article we propose a nonlocal cross-diffusion–fluid system describing the dynamics of multiple interacting populations living in a Newtonian fluid. First, we derive our nonlocal cross-diffusion–fluid system from a nonlocal kinetic-fluid model by the micro-macro decomposition method. Second, we prove the existence of weak solutions for the proposed system by applying the nonlinear Galerkin method with a priori estimates and compactness arguments. On the basis of micro-macro decomposition, we propose and develop an asymptotic-preserving numerical scheme. Finally, we discuss the computational results for the proposed system. [ABSTRACT FROM AUTHOR]