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In this episode, we explore two papers by Oriol Colomés and Santiago Badia that are exploring new algorithms to simulate complex fluid flows. Our focus is on the innovative Segregated Runge-Kutta (SRK) methods, a powerful approach for solving the incompressible Navier–Stokes equations.

Here's what you'll discover in this episode:

• The Core Innovation of SRK: Learn how SRK methods innovate in time integration by directly segregating velocity and pressure computations. This key architectural shift eliminates the need for traditional "fractional step" techniques that often limit accuracy, allowing SRK to maintain high-order accuracy for both velocity and pressure.
• Unlocking Scalability and Efficiency: We break down how SRK methods translate complex, coupled systems into simpler, uncoupled problems. This re-structuring is enables the use of optimal and highly scalable parallel solvers like Balancing Domain Decomposition by Constraints (BDDC) preconditioners. This means drastically reduced computational costs for large-scale simulations, with demonstrated weak scalability up to 8000 cores.
• Simulating Realistic Turbulent Flows More Efficiently: The conversation goes into SRK's application to Large Eddy Simulation (LES) of turbulent flows, particularly how it enables meaningful "wall-unresolved" simulations. By integrating weak imposition of boundary conditions with a novel "wall law", these methods allow engineers to use coarser meshes near solid boundaries, saving large computational resources without sacrificing accuracy in the bulk flow. This is crucial for problems like simulating flow around aircraft wings or in turbulent channels.
• Ensuring Accuracy and Robustness: We discuss how SRK methods preserve the discrete divergence constraint exactly in many practical scenarios, especially with weak boundary conditions, ensuring mass conservation. The episode highlights how these methods have been rigorously validated across diverse benchmarks, from the fundamental Taylor-Green vortex to complex turbulent flows around a NACA 0012 airfoil, showcasing their stability, accuracy, and real-world applicability.

Join us to understand how this work is pushing the boundaries of numerical simulation, offering a high-performance, accurate, and scalable computational framework for the next generation of fluid dynamics problems.

References

Colomés, O., & Badia, S. (2016). Segregated Runge–Kutta methods for the incompressible Navier–Stokes equations. International Journal for Numerical Methods in Engineering, 105(5), 372-400. https://doi.org/10.1002/nme.4987

Segregated Runge–Kutta methods for the incompressible Navier–Stokes equations

Colomés, O., & Badia, S. (2017). Segregated Runge–Kutta time integration of convection-stabilized mixed finite element schemes for wall-unresolved LES of incompressible flows. Computer Methods in Applied Mechanics and Engineering, 313, 189-215. https://doi.org/10.1016/j.cma.2016.09.040