An improved localized radial basis function meshless method for computational aeroacoustics

An improved localized radial basis function collocation method is developed for computational aeroacoustics, which is based on an improved localized RBF expansion using Hardy multiquadrics for the desired unknowns. The method approximates the spatial derivatives by RBF interpolation using a small set of nodes in the neighborhood of any data center. This approach yields the generation of a small interpolation matrix for each data center and hence advancing solutions in time will be of comparatively lower cost. An upwind implementation is further introduced to contain the hyperbolic property of the governing equations by using flux vector splitting method. The 4–6 low dispersion and low dissipation Runge–Kutta optimized scheme is used for temporal integration. Corresponding boundary conditions are enforced exactly at a discrete set of boundary nodes. The performances of the present method are demonstrated through their application to a variety of benchmark problems and are compared with the exact solutions.