Adaptive RBF-FD Meshless Solution of Two-Phase Flow Problems via Phase-Field Approach
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Two-phase flow problems are of considerable interest in many engineering applications, including chemical processing, environmental and mechanical engineering. The accurate numerical simulation of these flows is crucial for predicting system behaviour and optimizing performance. The physical features of two-phase flows, such as the presence of a moving interface and possible large differences in the thermophysical properties of the two phases, pose major challenges in the robust and accurate simulation of these problems. State-of-the-art simulations of two-phase flows are usually performed using mesh-based methods, such as the Finite Volume (FVM) or Finite Element (FEM) methods. However, adaptive re-meshing poses some limitations on the performance of these approaches, especially in the case of unstructured meshes. This presentation will highlight our latest results regarding the meshless simulation of two-phase flows with the Radial Basis Function-Finite Difference (RBF-FD) method. The geometric flexibility of this method fits perfectly with the context of two-phase problems where a moving interface needs to be continuously tracked. A phase-field technique, which leverages the Cahn-Hilliard equation, is used to model the evolution of the phase field describing the spatial distribution of the fluid phases. The dynamics of the considered two-phase flow problems is then fully described by coupling the Cahn-Hilliard equation with the Navier-Stokes equations. The time-dependent evolution of the flow is computed by means of an adaptive strategy by which the meshless node distribution is appropriately refined around the moving interface. This discretization approach allows the interface to be accurately captured throughout the whole simulation. Different benchmark problems are considered and the results are compared with literature and state-of-the-art numerical results, highlighting the potential of the RBF-FD method in the efficient and accurate solution of complex problems.
