An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation

The current paper is an improvement of the developed technique in Shu et al. (2005). The proposed improvement is to reduce the used CPU time for employing the local radial basis functions-differential quadrature (LRBF-DQ) method. To this end, the proper orthogonal decomposition technique has been combined with the LRBF-DQ technique. For checking the ability of the new procedure, the compressible Euler equation is solved. This equation has been classified in category of system of advection-diffusion equations. Moreover, several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme.