Meshless Approach for the Simulation of Compressible Isothermal Fluid Flows

In this work, we propose an explicit meshless approach based on the coupling of the Weighted Least Squares (WLS) method and the explicit Runge-Kutta (RK) scheme. This last scheme is used to approximate time derivatives while WLS approximation is used for spatial discretization. The proposed meshless approach offers several advantages over traditional methods. This approach provides a powerful tool for simulating compressible fluid flows, offering improved accuracy and computational efficiency compared to traditional methods. This approach is dedicated to the study of the flows of compressible isothermal fluids whose mathematical formulation is governed by the Navier-Stokes equations written in a strong formulation to avoid any difficulty in integration calculating. This meshless approach is tested on the classic example of a square cavity with a discussion on effects of the Mach number and the monomial basis order. The results are compared to those obtained using a traditional finite difference method.