Accurate discretization of diffusion in the LS-STAG cut-cell method using diamond cell techniques

摘要

In cut-cell methods for fluid flow in complex geometries such as the LS-STAG method (Nikfarjam et al. Comput Phys Commun 226:67-80, 2018), mesh non-orthogonality near the immersed boundary makes inaccurate 2-point formulas for computing the face-normal gradients in diffusive fluxes. A way to improve the accuracy is to compute the whole solution gradient at the cut-cell faces, thus decomposing the flux as an orthogonal contribution (using a standard 2-point formula) and non-orthogonal correction (using data at cell vertices). The solution at cut-cell vertices is then interpolated from cell-centered data and boundary conditions. This gradient reconstruction technique is commonly denominated "diamond cell method".