Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law

In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete level. We also present numerical experiments to study various limiting behavior of the numerical solutions.