Mesh Optimization for Improved Computational Fluid Dynamics Numerical Stability and Convergence Rate

Abstract:

A novel mesh optimization approach is utilized in conjunction with the Ansys Fluent solver for numerical stability and convergence rate enhancement of computational fluid dynamics simulations. This method leverages the dynamic mode decomposition of solution update vectors for solution mode identification. Through this data reduction technique, the large-scale linear evolution system is mapped onto a smaller space with substantially fewer degrees of freedom for stability analysis at a negligible fraction of the overall computational cost. The eigenanalysis of the small-scale matrix facilitates the identification of dominant solution modes during the simulation. This mesh optimization technique leverages the gradients of the problematic solution modes with respect to local changes of the mesh to calculate proper modification vectors for a small collection of nodes. These modifications lead to the improved numerical stability of the simulation. Employing the Ansys Fluent CFD package as the primary finite-volume solver, our study demonstrates the complete non-invasiveness of the presented mesh optimization approach, requiring no access to the underlying software architecture. The results presented herein illustrate the feasibility and efficacy of this mesh optimization technique in improving numerical stability and convergence rate, showcasing its compatibility with third-party flow solvers.