An improved fully one-sided diffuse-interface immersed boundary method with target-value reconstruction for compressible flows

Abstract

Although one-sided spreading has been shown to improve the near-wall accuracy of diffuse-interface immersed boundary methods (DIBMs), the effect of its asymmetric kernel support on the effective boundary location remains insufficiently understood. In this work, a detailed analysis of the one-sided spreading operator reveals an inward displacement of the effective boundary relative to the geometric boundary. To compensate for this displacement, a target-value reconstruction strategy is developed to ensure consistency between the values imposed at the effective boundary and the prescribed conditions at the geometric boundary. The strategy is incorporated into the fully one-sided diffuse-interface immersed boundary method (FODIBM) and applies to both Dirichlet and Neumann boundary conditions. Although confined to the target-value evaluation step, the modification substantially improves boundary-condition enforcement with negligible additional computational cost. Coupled with a hybrid lattice Boltzmann solver, the improved method consistently reduces L_2 and L_{\infty} error norms across different grid resolutions while retaining approximately second-order grid convergence. The no-slip and isothermal boundary-condition errors are reduced by 77% and 85%, respectively. Simulations involving various two- and three-dimensional geometries further show improved predictions relative to both the conventional DIBM and the original FODIBM. The results agree well with body-fitted reference solutions and experimental data, demonstrating accurate and computationally efficient simulations of compressible flows around complex geometries.