A meshfree collocation method for solving compressible isentropic Euler equations

The compressible isentropic Euler equations are a nonlinear system of hyperbolic conservation laws. In this paper, a meshfree collocation method based on compactly supported radial basis functions is proposed to solve the compressible isentropic Euler equations, which are expressed directly in terms of conservative variables and their derivatives. This method transforms the equations into a system of ordinary differential equations by differentiating the radial basis functions to approximate the spatial derivatives. The time discretization is performed using the classical explicit Runge–Kutta method. The application of periodic boundary conditions in the radial basis meshfree collocation method is discussed. Numerical examples demonstrate the effectiveness of this method in solving isentropic vortex convection problems with different boundary conditions. This method demonstrates good numerical accuracy for the smooth flow problems tested and provides a viable approach for solving hyperbolic systems using radial basis functions.