In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then, we apply a numerical flux function on the reduced problem. We present explicit conditions which such a numerical flux function needs to fulfill. These conditions guarantee the convergence to the weak entropy solution of the considered model class. Numerical examples validate our theoretical results and demonstrate that the approach can be applied to other nonlocal problems.

翻译：本文提出了一种较为通用的方法来近似求解非局部守恒律问题的解。首先，我们采用合适的数值积分规则对空间离散化中的非局部项进行近似；随后，将数值通量函数应用于简化后的问题。我们给出了此类数值通量函数所需满足的显式条件，这些条件保证了所考虑模型类解的弱熵解收敛性。数值算例验证了理论结果，并表明该方法可推广至其他非局部问题。