arXiv:2510.17500v3 Announce Type: replace Abstract: In this paper, a finite volume approximation scheme is used to solve a nonlocal macroscopic material flow model in two space dimensions, accounting for the presence of boundaries in the nonlocal terms. Based on a previous result for the scalar case, we extend the setting to a system of heterogeneous material on bounded domains. We prove the convergence of the approximate solutions constructed using the Roe scheme with dimensional splitting. We consider a regularized version of the flux function and establish BV bounds for a Roe-type scheme. Numerical tests show a good agreement with microscopic simulations.