Dionysios Angelidis

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

Simulation of wind turbine wakes on locally refined Cartesian Grids

Performing high-fidelity numerical simulations of turbulent flow in multi-turbine wind farms remains a challenging issue mainly because of the large computational resources required to accurately simulate the large disparity of spatial scales. To address this challenge we develop herein a new Adaptive Mesh Refinement (AMR) flow solver to enhance the resolution and improve the efficiency of the Virtual Wind Simulator (VWiS) code, which is capable of simulating multi-turbine wind farms in complex terrain. We extend the Curvilinear Immersed Boundary (CURVIB) approach incorporated in the VWiS code to unstructured Cartesian grids with strong coupling between multiple levels of refinement. The challenging issues of flux mismatching or pressure discontinuity across fine/coarse interfaces are overcome by the resulting fully unstructured approach. The efficiency and accuracy of the solver is demonstrated by solving the Navier-Stokes equations in driven cavity flows. Large-eddy simulation (LES) of turbulent flows past a stand alone wind turbine, which is modelled by using the Actuator Line Model (ALM), reveal that computed results obtained in locally refined domains are in good agreement with the experimental measurements. These simulations also show the ability of our method to simulate the rich dynamics on the wake of the turbine.