An efficient immersed boundary algorithm for simulation of flows in curved and moving geometries

• A simple and computationally efficient scheme is presented for: (a) tagging (while addressing moving/deforming boundaries) and (b) blanking redundant nodes in IBM.
• A hybrid MAC–SOLA solver is demonstrated and achieved better mass conservation and control over spurious fluctuation.
• Validation, verification and computational efficiency are demonstrated for a number of flow problems.

The applicability of immersed boundary method (IBM) in solving flow over complex and moving geometries is often restricted due to the computational overheads associated with the dynamic identification of immersed nodes and the high ratio of solid to fluid nodes. Furthermore, improper mass conservation and the unphysical pressure fluctuations result in large errors in IBM based flow predictions. Earlier attempts to overcome these issues were usually mathematically involved and computationally expensive. In the present paper, a simple and robust IBM implementation has been demonstrated which addresses these issues. The present method preserves the simplicity of sharp interface immersed boundary method and hence avoids complex coding logistics. This method uses a dynamic search algorithm for tagging of the immersed nodes and reduces the computational overheads. Mass conservation is ensured in the intercepted cells through a hybrid SOLA–MAC algorithm. The proposed algorithm iteratively satisfies the mass conservation equation in the intercepted cell and also eliminates spurious fluctuations in the temporal behavior of pressure. An overall second order accuracy is maintained in the discretization and interpolation schemes. The effectiveness and accuracy of the present scheme in handling the mass loss and spurious pressure fluctuation are demonstrated through a number of test cases. Comparisons are made with available experimental and numerical data for different external and internal flow problems.