Off-lattice interfacial force scheme for simulation of multiphase flows using meshless lattice Boltzmann method

Several off-lattice Boltzmann schemes have been proposed in the literature to generalize the classical lattice Boltzmann method to non-uniform and unstructured grids. Most of these methods can be categorized as the finite difference, finite volume, finite element, and meshless lattice Boltzmann methods. The main idea behind them has been to make the method more powerful and more efficient, particularly for domains with geometrically complex boundaries. However, there exist some issues with these methods. One of them is in the multiphase and multicomponent flows, in which the present methods of introducing interfacial forces are either confined to the lattice-based checkered grids, therefore they could not be used with general off-lattice Boltzmann methods, or are based on interface tracking techniques, which incorporate additional computational cost into the method. In this study, the meshless lattice Boltzmann method, introduced and developed by the authors, is extended to simulate multiphase flows. To do so, the pseudo-potential formulation of Shan and Chen is generalized so that it could be used for arbitrary node distributions without using any interface tracking method. To validate the proposed method, some of the basic static and dynamic multiphase problems are simulated. These problems include the Laplace test, the segregation test, the contact angle test, the two-phase Poiseuille flow, and finally, the droplet impingement on a solid surface. The results, which are compared with the existing analytical, experimental, and numerical results in the literature, illustrate the validation of the proposed method for the applied ranges of the Reynolds and Weber numbers. Although the present off-lattice interfacial force method is formulated for use with the meshless lattice Boltzmann method, it could be easily adapted to all off-lattice Boltzmann methods.