In this work, a discrete finite volume scheme (FVS) is developed for approximating a multidimensional agglomeration population balance equation on an unstructured grid. Previous applications of the FVS were restricted only to structured rectangular and triangular grids. The main hindrance of using the unstructured grid is less knowledge of the relation between the quality of solution and the nature of elements. The testing of the proposed FVS is conducted against the FVS on a structured grid using analytically tractable kernels. The numerical results reveal that the FVS with unstructured grid estimates the numerical results with higher accuracy and efficiency than the existing method. The use of unstructured grid offers improved numerical results due to the flexibility of placing the pivot in the space. Moreover, the mixing of components for a bicomponent population is examined using the variance of excess solute for the unstructured grid. (C) 2020 Published by Elsevier B.V.