Inverse distance weighting interpolation-based immersed boundary velocity correction method for incompressible flows

Abstract

In this work, the inverse distance weighting (IDW) interpolation is introduced into the implicit velocity correction-based immersed boundary method (IBM) for simulation of incompressible flows. In the original implicit velocity correction-based IBM, the solid body must be immersed in a uniform mesh region due to the use of the smooth Dirac delta function, which is utilized to associate Lagrangian points with their surrounding Eulerian points and only works with uniform meshes. The IDW method has the advantage that the interpolation range can be set flexibly. The introduction of the IDW interpolation can extend the application of the IBM to non-uniform meshes while reducing the number of Lagrangian points. The numerical test by the decaying vortex problem proves that the IDW interpolation does not significantly affect the overall accuracy of the IBM. In addition, numerical experiments for the flows around a circular cylinder and a NACA0012 airfoil demonstrate the advantages of the proposed method, including allowing fewer Lagrangian points while ensuring no streamline penetration to the solid body, as well as its adaptability to non-uniform meshes which can improve the computational efficiency due to the use of fewer mesh points. Finally, the simulation of the flow past a stationary sphere illustrates that the proposed method can effectively simulate the three-dimensional flow.