It is a pleasure to share this very recent paper by Jannes Hopman, Daniel Santos, Àdel Alsalti, Joaquim Rigola and myself:
J.A.Hopman, D.Santos, A.Alsalti-Baldellou, J.Rigola, and F.X.Trias. “Quantifying the checkerboard problem to reduce numerical dissipation”, Journal of Computational Physics, 521:113537, 2025. https://linkinghub.elsevier.com/retrieve/pii/S002199912400785X
In our latest research, we propose an innovative approach for managing checkerboard oscillations in incompressible flow simulations. Firstly, the lack of a proper definition for the checkerboard problem is addressed by proposing a novel physics-based coefficient. This coefficient, rooted in the disparity between the compact- and wide-stencil Laplacian operators, is able to quantify oscillatory solution fields with a physics-based, normalized, non-dimensional value. Secondly, a method to properly balance the checker-boarding and the numerical dissipation is proposed and tested: it employs the above-mentioned coefficient to establish a negative feedback between the level of checker-boarding and the inclusion of a pressure predictor. This novel method is tested for laminar and turbulent flows, demonstrating its capabilities in obtaining this dynamical balance without user intervention, achieving low numerical dissipation in absence of artificial oscillations.
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