A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method

A least-squares algorithm for handling complex boundaries with the lattice Boltzmann method is proposed. The method is an extension to an immersed boundary implementation of the solver. We impose additional rules that are designed to conserve the mass flux through cut-cell control volumes and also to satisfy the continuity condition on the numerical boundary points. Then, we use the least-squares method to find the best achievable solution of the overdetermined system. Further, computational cost assessments are considered. The qualitative and quantitative results show that the velocity values obtained from simulation of a flow with curved and moving boundaries, i.e., the Taylor-Couette flow, are closer to the exact solution than the values found from the traditional approach. Finally, we present some statistical analysis to show that the velocities are obtained confidently.