Lagrangian Vortex Particle Methods (LVPM) are well-suited for simulation of unsteady vortex-dominated incompressible fluid flow in the moderate Reynolds number regime, including transitional flow. Key advantages of LVPM are (1) near absence of numerical diffusion, thanks to the Lagrangian accounting of convection; (2) dynamic solution adaptivity resulting from the inherent ability of vortex elements to automatically convect toward regions with high vorticity strength; and (3) excellent capacity for high-efficiency parallelization and vectorization due to the high arithmetic intensity of the Biot-Savart formulation. However, accurate and efficient treatment of the flow near the boundary, which invariably requires the use of anisotropic vortex elements, has remained mostly elusive to date.On the other hand, compact high-order Eulerian CFD methods have recently demonstrated excellent accuracy and computational efficiency on canonical problems; however, they are rather challenging to apply to problems that involve multiple bodies in relative motion, such as those observed in many cardiovascular devices.To this end, leveraging the best attributes of these two very diverse approaches, we demonstrate a new open-source hybrid CFD solver, which combines a vorticity-based high-order Eulerian method for accurate prediction of the near-body flow with a LVPM for off-body CFD to solve unsteady incompressible flow in complex geometries. This paper will focus on the hybridization of the Eulerian and Lagrangian solutions in a smooth and accurate manner. An accompanying paper “A High-Order Flux Reconstruction Method for 2-D Vorticity Transport” will discuss the Eulerian solution in more detail.The computational domain for the Eulerian solver covers only a layer above any wall boundaries, and ends in an open boundary to the Lagrangian regime. Lagrangian vortex particles can exist in both domains. In one single outer time step, the LVPM marches ahead to provide the velocity and vorticity boundary conditions on the open boundary of the high-order mesh. The high-order Eulerian solver then simulates that same outer time step over a larger number of inner time steps, each involving solutions of convection, diffusion, and a Poisson solution for the vorticity-velocity inversion. At the end of those substeps, the vorticity in the Eulerian domain is used to reset strengths on any co-located vortex particles. The vortex particles then help reset any discontinuities in the vorticity in the outer reaches of the Eulerian domain. In this manner, vorticity is able to smoothly exit and enter the Eulerian domain while still far more accurately modeling the high gradients expected near the wall.To study the performance and accuracy of the proposed method, we simulated several canonical viscous flow problems such as the 2-D lid-driven cavity and an impulsively started circular cylinder at Re = 1,000 and 9,500. The new method is shown to be able to resolve near-wall regions that would have required a far-more computationally-intense purely Lagrangian solution, ensuring long-term accuracy of viscous vortical flows.

A Hybrid High-Order Vorticity-Based Eulerian and Lagrangian Vortex Particle Method, the 2-D Case

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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