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We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked using a volume fraction function. The volume fraction is advected using a method based on the minimisation of a directional flux-based error. For stability, the advection terms are discretised using upwinding schemes. In the vicinity of the embedded geometries, the signed distance function is used to populate the surface of the geometries to generate a body-conforming point cloud. Consequently, the points on the boundaries participate directly in the discretisation, unlike conventional immersed-boundary methods where they are either used to calculate momentum deficit (for example, continuous forcing) or conservation losses (for example, cut-cell methods). The boundary conditions are, therefore, directly imposed at these points on the embedded geometries, opening up the possibility for a discretisation that is body-conforming and spatially varying in resolution, while retaining the consistency of the scheme. We present benchmark test cases that validate the method for two-phase flows, flows with embedded boundaries and a combination of both.

In this paper, a new method to model solidification of thin liquid films is proposed. \blue{This method is targeted at applications like aircraft icing and tablet coating where the formation of liquid films from impinging droplets on a surface form a critical part of the physics of the process.} The proposed model takes into account the (i) unsteadiness in temperature distribution, (ii) heat transfer at the interface between the solid and the surface, (iii) volumetric expansion/contraction and (iv) the liquid thin-film behaviour, each of which are either partly or fully ignored in existing models. The liquid thin-film, modeled using the Discrete Droplet Method (DDM), is represented as a collection of discrete droplets that are tracked in a Lagrangian sense. The height of the liquid film is estimated as a summation of Gaussian kernel functions associated with each droplet. At each droplet location, a solid height is also computed. The evolution of the solid height is governed by the Stefan problem. The flow of the liquid thin-film is solved just as in the case of DDM, while also taking into consideration the shape of the solidified region lying beneath the droplet. The results presented in this work show the reliability of the proposed model in simulating solidification of thin-films and its applicability to complex problems such as ice-formation on aircraft wings. The model has been verified for canonical problems that have analytical solutions. For the more complex problems of icing, the results of the model are compared with data from literature, without considering a background air flow. The comparison can be improved by coupling this model with suitable air flow solvers, as shown in the final test case., Comment: Pre-proof version

In this paper, we look at the pressure checkerboard problem that arises in an Eulerian meshless method that solves the incompressible Navier-Stokes equations using the generalized finite difference method (GFDM). Although, the checkerboard problem has been dealt with extensively in mesh-based methods, the literature in connection with meshless methods is comparatively scarce. In this paper, we explore the occurrence of the checkerboard problem in a meshless method. A few unsuccessful attempts to resolve the checkerboard problem are reported. The successful fix for the problem entails an algorithm that adapts the point cloud by adding points in the regions of pressure oscillations. The algorithm uses an error indicator that detects the presence of the checkerboard oscillations in the solution. The algorithm minimizes the computational effort since it ensures the use of additional points only in regions of concern, as directed by the error indicator, in contrast to an approach of using a highly refined set of points throughout the domain. It also requires no a priori estimates of the regions where the oscillations occur and integrates conveniently in the framework of the meshless method since no re-meshing strategies are involved. The results are compared with literature and a good match is observed.

In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3D resolved Navier Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.