Boundary layer equation-enhanced immersed boundary method for simulation of incompressible flows

A boundary layer equation-enhanced immersed boundary method (IBM) is proposed in this work to simulate incompressible flows. This method firstly introduces a virtual body-fitted grid along the boundary and utilizes it to transfer the influence of the boundary to the flow field. Then, the flow field is predicted using the finite volume method combined with the lattice Boltzmann flux solver. Subsequently, the simplified boundary-layer equations are solved to calculate the wall shear stress, which is then combined with the no-slip condition to reconstruct the velocity on the virtual grid. Finally, the reconstructed velocity is mapped onto the underlying Eulerian mesh to update the flow field. The introduction of the boundary-layer equation enhances the local accuracy near the wall. Numerical experiments on the flows past a NACA 0012 airfoil demonstrate that the proposed IBM captures the thin boundary layer with steep velocity gradients more effectively than the conventional diffuse-interface IBM. Additionally, different from the conventional sharp-interface IBM, the proposed IBM treats the mesh cells inside and outside the boundary uniformly, preventing the mesh cell discontinuities near the boundary. This feature enables the proposed IBM to handle moving boundary problems without experiencing spurious oscillations, as verified through the simulation of flow past a heaving NACA 0012 airfoil.