Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation. (English) Zbl 1416.65298
Summary: In this work, we introduce the convergence analysis of the recently developed finite volume scheme to solve a pure aggregation population balance equation that is of substantial interest in many areas such as chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. The notion of the finite volume scheme is to conserve total mass of the particles in the system by introducing weight in the formulation. The consistency of the finite volume scheme is also analyzed thoroughly as it is an influential factor. The convergence study of the numerical scheme shows second order convergence on uniform, nonuniform smooth (geometric) as well as on locally uniform meshes independent of the aggregation kernel. Moreover, the first-order convergence is shown when the finite volume scheme is implemented on oscillatory and random meshes. In order to check the accuracy, the numerical experimental order of convergence is also computed for the physically relevant as well as analytically tractable kernels and validated against its analytical results.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35R09 | Integro-partial differential equations |
| 65R20 | Numerical methods for integral equations |
Keywords:
consistency; convergence; finite volume scheme; integro-partial differential equations; numerical analysis; nonlinear population balance equationReferences:
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