In this work, two new number‐ and volume‐consistent finite volume methods for the numerical solution of binary and multifragmentation problems are introduced. The new number‐consistency is achieved by introducing a single weight function. Several benchmark problems of different complexity are solved to assess the accuracy. Mathematical convergence analysis suggests that both of the new methods are numerically second order convergent with respect to the grid size on uniform and nonuniform meshes.

中文翻译：

---

粒子破碎模型的有限体积方法的改进的准确性和收敛性分析

在这项工作中，引入了两种新的数量和体积一致的有限体积方法，用于二元和多重碎片问题的数值解。通过引入单个权重函数可以实现新的数字一致性。解决了几个复杂度不同的基准问题，以评估准确性。数学收敛分析表明，相对于均匀和非均匀网格上的网格大小，这两种新方法在数值上都是二阶收敛。