Numerical solution of the two-phase incompressible Navier–Stokes equations using a GPU-accelerated meshless method

This paper presents the development and implementation of a Meshless two-phase incompressible fluid flow solver and its acceleration using the graphics processing unit (GPU). The solver is formulated as a Localized Radial-Basis Function Collocation Meshless Method and the interface of the two-phase flow is captured using an implementation of the Level-Set method. The Compute Unified Device Architecture (CUDA) language for general-purpose computing on the GPU is used to accelerate the solver. Through the combined use of the LRC Meshless method and GPU acceleration this paper seeks to address the issue of robustness and speed in computational fluid dynamics. Traditional mesh-based methods require extensive and time-consuming user input for the generation and verification of a computational mesh. The LRC meshless method seeks to mitigate this issue through the use of a set of scattered points that need not meet stringent geometric requirements like those required by finite-volume and finite-element methods, such as connectivity and poligonalization. The method is shown to render very accurate and stable solutions and the implementation of the solver on the GPU is shown to accelerate the solution by several orders.