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Abstract

In computational fluid dynamics (CFD), mesh quality plays a critical role in ensuring solution stability. However, as simulations scale to larger and more complex meshes, assessing mesh reliability solely through solver convergence becomes impractical; instabilities often emerge only after significant computational cost. Our in-house mesher employs state-of-the-art mesh generation algorithms and a robust mesh quality assessment process. Yet, even when all conventional quality criteria are satisfied, non-convergent simulations can still occur, revealing that geometric quality alone does not guarantee stability. This motivates the need for topology based indicators that can predict and improve stability prior to solving. This work investigates how modifying mesh topology can enhance stability in unstructured triangular meshes. Specifically, Uniform Degree Swapping (UDS) is applied as a systematic approach to reduce variability of vertex degree (the number of cells that meet at each vertex). These topological adjustments lead to improvements in the mapping between control volume average solution values used to evaluate fluxes in the finite volume flow solver, which has been shown previously to improve stability. A robust relationship is observed between a more uniform neighbor count and lower norms for this mapping, indicating enhanced stability potential. Results from Burgers’ and Euler test cases validate this relationship. Among six Burgers’ meshes, four became stable after UDS, while two already stable meshes exhibited faster convergence. Similarly, three previously unstable Euler meshes reached stability only after UDS. Although one case remained unstable, its residuals decreased by approximately a factor of three (63% reduction). Overall, the findings demonstrate that improving mesh topology can promote faster, more stable convergence in unstructured CFD simulations.