A meshless Radial Basis Method (RBM) for solving the detailed population balance equation

•A novel meshless Radial Basis Method (RBM) is introduced for solving the PBE.•The RBM solves the PBE for growth, nucleation, breakage and aggregation.•The MQ RBF is used to expand the number density function at the collocation points.•The RBM is validated analytically and numerically for stirred tank reactors.•The RBM is attractive and very efficient in terms of CPU requirement and accuracy. The Radial Basis Method (RBM) is introduced for solving the Population Balance Equation (PBE). In this method, the continuous number density function is approximated by a series of symmetric multiquadric basis functions at selected global collocation points along the internal coordinates. Therefore, the RBM is considered as a meshless method. The RBM is convenient and suitable for complex problems involving nucleation, growth, breakage and aggregation phenomena. The method provides naturally a continuously differentiable, or “smooth”, solution and avoids solving ill-conditioned problems. The numerical solutions are validated analytically and numerically using different case-studies for uniform stirred-tank. For these examples, 20 collocation points were found to be enough to achieve accurate predictions. The RBM ability to predict multimodal distribution functions and moving steep fronts is moreover highlighted. The proposed method proves to be very efficient for solving the detailed PBE in terms of accuracy, stability and CPU time requirements.