An Exception Algorithm to Ease Convergence in Multistage Turbomachinery Throughflow Calculations

Abstract Iterative solvers used in turbomachinery, spanning throughflow formulations and higher-order computational fluid dynamics (CFD), depend critically on how they are initialized. The starting state determines not only the number of iterations but often whether a solution is found at all when residuals are noisy or non-smooth. In such regimes, fast gradient updates can stall, oscillate, or violate bounds even when the underlying model is sound. This work introduces a solver-level exception algorithm that detects those failure signatures at run time and temporarily replaces the gradient step with a bounded, derivative-free fallback to reestablish a safe descent under strict feasibility limits. Control is returned to the fast path once a reliable reduction is found, preserving turnaround time in easy regions while adding robustness where the reference update is untrustworthy. The practical motivation is to reduce user workload and eliminate manual operating-point marching while enabling wider off-design coverage and characteristics traverses without a discernible accuracy or speed penalty. Although illustrated within a streamline curvature throughflow solver, the approach is general and can be interfaced with other throughflow methodologies and, more broadly, with higher-order CFD. Validation on single- and multistage axial-flow turbines shows improved robustness without a discernible accuracy or speed penalty within a state-of-the-art throughflow environment.