Residual-Guided Adaptive Pressure Bases for Dimension-Reduced FLIP Projection

We present a residual-guided adaptive pressure basis for dimension-reduced FLIP liquid simulation. Uniform dimension reduction lowers the cost of the pressure Poisson solve, but aggressive coarsening can under-represent localized pressure variation near impacts, thin sheets, and complex free surfaces. Our method augments the coarse surface-aware pressure basis only in regions predicted to require additional representation capacity. The selection criterion combines the fine-grid residual of the reduced pressure solution with free-surface curvature and local velocity variation. To avoid a same-frame refinement re-solve, the filtered residual from the previous time step is used as a temporal predictor, while the geometric and kinematic indicators respond to newly formed structures. The resulting adaptive system requires a single reduced pressure solve per time step. Comparisons with uniform dimension reduction and full-resolution projection show lower pressure approximation error and post-projection divergence than uniform reduction with only a modest increase in pressure degrees of freedom and computation time. The same formulation is evaluated in both 2D and 3D FLIP simulations.