I. Akkerman

Isogeometric analysis of free-surface flow

Abstract This paper presents the first application of isogeometric analysis, a new computational technology built on higher-order and higher-continuity basis functions employed in Computer-Aided Design and computer graphics, to the computation of free-surface phenomena described using the level set approach. The method is based on the variational framework that is suitable for discretization by standard finite elements as well as the basis functions employed in isogeometric analysis. The underlying numerical formulation globally conserves mass and preserves a sharp air–water interface for the entire length of the simulation. The numerical tests indicate that the proposed methodology gives an accurate description of the free-surface behavior in both quasi-steady and dynamic regimes. Furthermore, very good per-degree-of-freedom accuracy is obtained when higher-order and higher-continuity isogeometric discretizations are employed in free-surface computations.

Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics

Abstract : This paper presents our approach for the computation of free-surface/rigid-body interaction phenomena with emphasis on ship hydrodynamics. We adopt the level set approach to capture the free-surface. The rigid body is described using six-degree-of-freedom equations of motion. An interface-tracking method is used to handle the interface between the moving rigid body and the fluid domain. An Arbitrary Lagrangian Eulerian version of the residual-based variational multiscale formulation for the Navier Stokes and level set equations is employed in order to accommodate the fluid domain motion. The free-surface/rigid body problem is formulated and solved in a fully coupled fashion. The numerical results illustrate the accuracy and robustness of the proposed approach.

STRUCTURAL MECHANICS MODELING AND FSI SIMULATION OF WIND TURBINES

A fluid–structure interaction (FSI) validation study of the Micon 65/13M wind turbine with Sandia CX-100 composite blades is presented. A rotation-free isogeometric shell formulation is used to model the blade structure, while the aerodynamics formulation makes use of the FEM-based ALE-VMS method. The structural mechanics formulation is validated by means of eigenfrequency analysis of the CX-100 blade. For the coupling between the fluid and structural mechanics domains, a nonmatching discretization approach is adopted. The simulations are done at realistic wind conditions and rotor speeds. The rotor-tower interaction that influences the aerodynamic torque is captured. The computed aerodynamic torque generated by the Micon 65/13M wind turbine compares well with that obtained from on-land experimental tests.

A conservative level set method suitable for variable-order approximations and unstructured meshes

This paper presents a formulation for free-surface computations capable of handling complex phenomena, such as wave breaking, without excessive mass loss or smearing of the interface. The formulation is suitable for discretizations using finite elements of any topology and order, or other approaches such as isogeometric and finite volume methods. Furthermore, the approach builds on standard level set tools and can therefore be used to augment existing implementations of level set methods with discrete conservation properties. Implementations of the method are tested on several difficult two- and three-dimensional problems, including two incompressible air/water flow problems with available experimental results. Linear and quadratic approximations on unstructured tetrahedral and trilinear approximations on hexahedral meshes were tested. Global conservation and agreement with experiments as well as computations by other researchers are obtained.

Aerodynamic Simulation of Vertical-Axis Wind Turbines

Full-scale, 3D, time-dependent aerodynamics modeling and simulation of a Darrieus-type vertical-axis wind turbine (VAWT) is presented. The simulations are performed using a moving-domain finite-element-based ALE-VMS technique augmented with a sliding-interface formulation to handle the rotor-stator interactions present. We simulate a single VAWT using a sequence of meshes with increased resolution to assess the computational requirements for this class of problems. The computational results are in good agreement with experimental data. We also perform a computation of two side-by-side counterrotating VAWTs to illustrate how the ALE-VMS technique may be used for the simulation of multiple turbines placed in arrays.

Isogeometric analysis of Lagrangian hydrodynamics: Axisymmetric formulation in the rz-cylindrical coordinates

A recent Isogeometric Analysis (IGA) formulation of Lagrangian shock hydrodynamics [4] is extended to the 3D axisymmetric case. The Euler equations of compressible hydrodynamics are formulated using the rz-cylindrical coordinates, and are discretized in the weak form using NURBS-based IGA. Artificial shock viscosity and internal energy projection are added to stabilize the formulation. The resulting discretization exhibits good accuracy and robustness properties. It also gives exact symmetry preservation on the appropriately constructed meshes. Several benchmark examples are computed to examine the performance of the proposed formulation.

Large-Eddy Simulation of Shallow Water Langmuir Turbulence Using Isogeometric Analysis and the Residual-Based Variational Multiscale Method

Abstract : We develop a residual-based variational multiscale (RBVMS) method based on isogeometric analysis for large-eddy simulation (LES) of wind-driven shear flow with Langmuir circulation (LC). Isogeometric analysis refers to our use of NURBS (Non-Uniform Rational B-splines) basis functions which have been proven to be highly accurate in LES of turbulent flows (Bazilevs, Y., et al. 2007, Comput. Methods Appl. Mech. Eng., 197, pp. 173 201). LC consists of stream-wise vortices in the direction of the wind acting as a secondary flow structure to the primary, mean component of the flow driven by the wind. LC results from surface wave-current interaction and often occurs within the upper ocean mixed layer over deep water and in coastal shelf regions under wind speeds greater than 3m s 1. Our LES of wind-driven shallow water flow with LC is representative of a coastal shelf flow where LC extends to the bottom and interacts with the sea bed boundary layer. The governing LES equations are the Craik-Leivobich equations (Tejada-Mart nez, A. E., and Grosch, C. E., 2007, J. Fluid Mech., 576, pp. 63 108; Gargett, A. E., 2004, Science, 306, pp. 1925 1928), consisting of the time-filtered Navier-Stokes equations. These equations possess the same structure as the Navier-Stokes equations with an extra vortex force term accounting for wave-current interaction giving rise to LC. The RBVMS method with quadratic NURBS is shown to possess good convergence characteristics in wind-driven flow with LC. Furthermore, the method yields LC structures in good agreement with those computed with the spectral method in (Thorpe, S. A., 2004, Annu. Rev. Fluids Mech., 36, pp. 584 55 79) and measured during field observations in (D Alessio, S. J., et al., 1998, J. Phys. Oceanogr., 28, pp. 1624 1641; Kantha, L., and Clayson, C. A., 2004, Ocean Modelling, 6, pp. 101 124). [DOI: 10.1115/1.4005059]

Monotone level-sets on arbitrary meshes without redistancing

Abstract In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary meshes. We show that the regularized Heaviside function can be non-smooth on non-uniform meshes. Alternative regularizing definitions that are indeed smooth and monotonic, are introduced. These new definitions lead to smooth Heaviside functions by taking the changing local meshsize into account. The second issue is the computational cost and fragility caused by the necessity of redistancing the level-set field. In [1, 2] it is shown that strongly coupling the level-set convection with the flow solver provides robustness and potentially efficiency and accuracy advantages. The next step would be to include redistancing within the strong coupling part of the algorithm. The computational cost of current redistancing procedure prohibit this. Four alternative approaches for circumventing the expensive redistancing step are proposed. This should facilitate a fully coupled level-set approach. Some benchmark cases demonstrate the efficacy of the proposed approaches. These includes the standard test case of the vortex in a box. Based on these results the most favourable redistancing approach is selected.

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective–diffusive context

This paper presents the construction of novel stabilized finite element methods in the convective–diffusive context that exhibit correct-energy behavior. Classical stabilized formulations can create unwanted artificial energy. Our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small-scales within the variational multiscale framework (VMS). The desire for correct energy indicates that the large- and small-scales should be H 0 1 -orthogonal. Using this orthogonality the VMS method can be converted into the streamline-upwind Petrov–Galerkin (SUPG) or the Galerkin/least-squares (GLS) method. Incorporating both large- and small-scales in the energy definition asks for dynamic behavior of the small-scales. Therefore, the large- and small-scales are treated as separate equations. Two consistent variational formulations which depict correct-energy behavior are proposed: (i) the Galerkin/least-squares method with dynamic small-scales (GLSD) and (ii) the dynamic orthogonal formulation (DO). The methods are presented in combination with an energy-decaying generalized-α time-integrator. Numerical verification shows that dissipation due to the small-scales in classical stabilized methods can become negative, on both a local and a global scale. The results show that without loss of accuracy the correct-energy behavior can be recovered by the proposed methods. The computations employ NURBS-based isogeometric analysis for the spatial discretization.

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. : II: The incompressible Navier–Stokes equations

This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective-diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. The convective-diffusive context, CMAME, Accepted 2018]. This work extends ideas of this paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection-diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin (SUPG) and the Galerkin/least-squares method (GLS). The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large- and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.