A curvature-corrected immersion boundary method for adaptive Cartesian meshes

In Cartesian grid methods, the non-body-fitted nature between orthogonal grids and complex solid boundaries poses a significant challenge for accurately imposing boundary conditions, which directly impacts simulation accuracy. The proposed method addresses this by locating reference points along the outward normal direction of the boundary surface, applying bilinear interpolation to obtain the flow variables at those points, and incorporating local curvature information to extrapolate physical quantities. This approach enables accurate reconstruction of flow variables in virtual cells near the boundary, particularly enhancing accuracy in regions with high curvature. Validation on multiple benchmark cases demonstrates a substantial reduction in boundary-induced errors, with errors in the $L_1$, $L_2$ and $L_{\mathrm{\infty }}$ norms decreasing by approximately an order of magnitude. The overall method retains second-order convergence and effectively suppresses spurious entropy generation in regions of high curvature, offering a reliable and efficient boundary treatment for Cartesian-grid CFD simulations of complex geometries.