On a symmetry-preserving unconditionally stable projection method on collocated unstructured grids for incompressible flows

It is a pleasure to share this very recent paper by Dani Santos, Jannes Hopman, Carlos David Pérez Segarra and myself:

D.Santos, J.A.Hopman, C.D.Pérez-Segarra, and F.X.Trias. “On a symmetry-preserving unconditionally stable projection method on collocated unstructured grids for incompressible flows”, Journal of Computational Physics, 523:113631, 2025. https://lnkd.in/dmDj9aeH

Scale-resolving simulations of turbulent flows in complex geometries are often performed on collocated unstructured meshes. However, the main challenge with this approach is the pressure-velocity coupling. Reconciling numerical stability with physical accuracy is far from straightforward. Standard solutions frequently introduce excessive artificial dissipation, which compromises the turbulence dynamics. Conversely, attempts to eliminate this non-physical dissipation may lead to instability, particularly in the presence of highly distorted grid elements.

In this context, this work defines the conditions for a symmetry-preserving, unconditionally stable projection method for incompressible flows, such as PISO or the Fractional Step Method, on collocated unstructured grids. The formulation focuses on preserving the inherent symmetries of the differential operators. Furthermore, a general theorem is proven for these projection methods, outlining the mathematical requirements for the operators and the geometric conditions the mesh must satisfy, even in cases of extreme distortion. Numerical tests on highly distorted meshes confirm the robustness and stability of the proposed method.