Pressure-Robust Adaptive RBF-FD Discretizations for High-Reynolds Incompressible Navier–Stokes Flows on Irregular Domains

الملخص

Pressure-robust Navier–Stokes analyses are well developed in compatible mesh-based methods, while current meshless studies emphasize geometric flexibility, divergence control, or high-Reynolds stabilization. Their integration with residual-driven RBF-FD node adaptation on irregular domains remains insufficiently developed. A pressure-robust adaptive RBF-FD framework (PR-A-RBF-FD) was formulated in two dimensions. A streamfunction–vorticity branch removes pressure by a curl-filtered forcing, and an adjoint-compatible mixed Oseen branch tests discrete pressure pollution. Polyharmonic splines with polynomial augmentation generated local operators; residual indicators inserted Halton nodes in vortical and convective regions. Damped Newton and stabilized Oseen solves were evaluated on a wavy level-set domain and a perforated domain. Changing pressure amplitude from 1 to 10⁶ produced zero velocity change at Re = 100, 500, and 1000. For compatible discrete-gradient loads, the normalized pollution coefficient decreased from 6.696e-02 to at most 6.124e-17, a factor exceeding 1.1e+15. With 380 matched nodes, adaptivity reduced velocity RMS error by 88.7%, 75.2%, and 67.0% at Re = 100, 500, and 1000. A 1056-node nonlinear manufactured test retained velocity errors between 7.35×10⁻⁴ and 3.58×10⁻² for Re = 100–5000. The compatible load treatment removes discrete pressure pollution when the load is represented in the matching gradient range, and residual-driven node placement substantially improves matched-size accuracy. The results support a modern meshless research direction, while also identifying sensitivity to independently sampled gradients, node-cloud quality, and nonlinear initialization.