An accurate immersed boundary method using radial-basis functions for incompressible flows

Abstract

In this work, we introduce a parallel computational solver based on the sharp-interface immersed boundary method for simulating three-dimensional incompressible flows over stationary and moving boundaries. Despite the robustness and ease of implementation of conventional body-conformal grid methods, they are limited to relatively simple immersed geometries, leading to challenges in grid generation and quality. Our approach employs a multi-dimensional ghost-cell methodology and radial basis functions interpolation/splines to achieve accurate boundary condition and superior efficiency. We utilize unstructured triangular elements for geometric surface discretization and non-uniform Cartesian grids for constructing flow domains around the immersed boundaries. Furthermore, full parallelization using domain decomposition ensures scalability on distributed memory platforms, facilitated through message-passing interface libraries. Additionally, we introduce a flow smoothing strategy to mitigate spurious pressure oscillations near immersed bodies. Through simulations of two- and three-dimensional fluid-structure interaction problems, we demonstrate the effectiveness, accuracy, and efficiency of our computational solver.