Adaptive meshless local maximum-entropy finite element method for Navier-Stokes equations

Based on the successful application of the adaptive meshless local maximum-entropy finite element method to solve the convection-diffusion equation, this study extends the same principle to study the 2-dimensional Navier-Stokes equations. Through extensive case studies, this work demonstrates that the present approach is a viable alternative to resolve the high Reynolds number Navier-Stokes equations. The simulation results indicate that by incorporating additional points into the elements without increasing the bandwidth or refinement via the local maximum-entropy procedure, it will enhance the accuracy and efficiency of numerical simulations. A 2-dimensional square lid-driven cavity with various Reynolds numbers will serve as the first example. In the second example, we address a more complex geometry by solving the cavity with a hole inside the cavity center. The numerical results of the model compare favorably with other numerical solutions, including the finite difference method and the finite element method. This paper provides a very powerful tool to study the boundary layer theory with irregular geometry of the Navier-Stokes equations.