A novel RBF-DDM method for modelling transient droplet spreading in simple oil shear flow

This current numerical model of droplet spreading in a simple oil shear flow is assessed using a hybrid combination of the radial basis function (RBF) and domain decomposition method (DDM). The complex interfacial interaction understanding of oil-water is challenging to consider appropriately with the RBF-DDM numerical solution. The governing equations, which consist of the Navier-Stokes equation in primitive variable form, the Cahn-Hilliard equation, and the Poisson equation, are solved using the Radial Basis Function (RBF) method for spatial derivatives and the forward Euler method for time derivatives. This combination of RBF and DDM successfully addressed the complex domain multifluid interaction, with the dense matrix solved in several subdomains. The capillary number (Ca) and initial oil velocity are two independent variables analyzed, with the deformation coefficient serving as the primary dependent variable. The findings reveal that both variables affect the deformation coefficient presented with the deformation based on non-dimensionalization time. As theoretically stated, the interfacial tension is inversely proportional to the Ca, meaning that a possibly high Ca leads to a higher deformation coefficient. To get accurate elaboration, the convergence analysis and statistical model analysis use root mean square divergence (RMSDIV) and root mean square error (RMSE), respectively.