Numerical solution of backward-facing step flow by a high-order radial-basis-function-based method

The backward-facing step flow is commonly known as a standardized benchmark test to validate any numerical schemes. In this paper, we present a numerical method to predict and identify the flow separation and wakes of the backward-facing step flow. The numerical method is derived from the approximation of high-order derivatives by a summation of weighted radial basis functions (RBF). More specifically, our method plans to approximate spatially up to the second derivatives thanks to gathering the desired information of two adjacent nodes. In terms of temporal approximation, Adams-Bashforth method is applied to convection terms while Crank-Nicolson method is used for diffusion terms. The numerical solution is then compared to the previously published results for verification purposes. All solutions are in good agreement with published benchmark tests which demonstrate the robustness of RBF-based approximation.