We give a brief introduction to research on adaptive computational methods for laminar compressible and incompressible flows and then focus on computability and adaptivity for turbulent incompressible flow, where we present a framework for adaptive finite element methods with duality-based a posteriori error control for chosen output quantities of interest. We show in concrete examples that outputs such as mean values in time of drag and lift of a bluff body in a turbulent flow are computable to a tolerance of a few percent, for a simple geometry using some hundred thousand mesh points and for complex geometries using some million mesh points.

We present a framework for coupled multiphysics in computational fluid dynamics, targeting massively parallel systems. Our strategy is based on general problem formulations in the form of partial differential equations and the finite element method, which open for automation, and optimization of a set of fundamental algorithms. We describe these algorithms, including finite element matrix assembly, adaptive mesh refinement and mesh smoothing; and multiphysics coupling methodologies such as unified continuum fluid-structure interaction (FSI), and aeroacoustics by coupled acoustic analogies. The framework is implemented as FEniCS open source software components, optimized for massively parallel computing. Examples of applications are presented, including simulation of aeroacoustic noise generated by an airplane landing gear, simulation of the blood flow in the human heart, and simulation of the human voice organ.

This work presents a direct comparison of unsteady, turbulent flow simulations with measurements performed using a Gulfstream G550 nose landing gear model. The experimental campaign, which was carried out by researchers from the NASA Langley Research Center, provided a series of detailed, well documented wind-tunnel measurements for comparison and validation of computational fluid dynamics (CFD) and computational aeroacoustics (CAA) methodologies. Several computational efforts were collected and presented at the Benchmark for Airframe Noise Computation workshops, BANC-I and II. For our simulations, we used a General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh is adaptively refined with respect to a posteriori estimates of the error in a quantity of interest, here the source term in Lighthill's equation. The mesh is fully unstructured and the solution is time-resolved, which are key ingredients for solving problems of industrial relevance in the field of aeroacoustics. Moreover, we choose to model the boundary layers on the landing gear geometry with a free-slip condition for the velocity, which we previously observed to produce good results for external flows at high Reynolds numbers, and which considerably reduces the amount of cells required in the mesh. The comparisons presented here are an attempt to quantify the accuracy of our models, methods and assumptions; to that end, several results containing both time-averaged and unsteady flow quantities, always side by side with corresponding experimental values, are reported. The main finding is that we are able to simulate a complex, unsteady flow problem using a parameter-free methodology developed for high Reynolds numbers, external aerodynamics and aeroacoustics applications.

Offshore floating platforms for wind turbines represent challenging concepts for designers trying to combine an optimal compromise between cost effectiveness and performance. Modelling of the hydrodynamic behaviour of the structure is still the subject of wide debate in the technical communities. The assessment of the hydrodynamics of the support structure is not an easy task as the floaters consist of an assembly of columns, braces and pontoons, commonly also with heave plates: Each of these components corresponds to a different hydrodynamic model and it further interacts with the other elements. This results in very complex non-linear modeling, which makes it necessary to resort to computational fluid dynamics (CFD) methods for the evaluation of the combined hydrodynamics. In the framework of the collaboration between the Basque Centre for Applied Mathematics (BCAM) and Tecnalia R&I, the interaction of the sea flow with a semisubmersible floating offshore wind platform have been calculated by using the open source solver Unicorn in the FEniCS-HPC framework when subject to a steady inflow. The prototype of the platform consists in a semi-submersible 4-columns column stabilized platform - NAUTILUS Floating Solutions concept-; columns are connected by a rigid ring pontoon provided with heave damping plates at the bottom. The novelty of the approach in FEniCS-HPC hinges upon an implicit formulation for the turbulence, a cheap free slip model of the boundary layer and goal-oriented mesh adaptivity [8, 6, 9, 20, 1]. We find that the results are consistent with experimental results for cylinders at high Reynolds number.

This paper presents a summary of the computational predictions and measurement data contributed to Category 7 of the 3rd AIAA Workshop on Benchmark Problems for Airframe Noise Computations (BANC-III), which was held in Atlanta, GA, on June 14-15, 2014. Category 7 represents the first slat-noise configuration to be investigated under the BANC series of workshops, namely, the 30P30N two-dimensional high-lift model (with a slat contour that was slightly modified to enable unsteady pressure measurements) at an angle of attack that is relevant to approach conditions. Originally developed for a CFD challenge workshop to assess computational fluid dynamics techniques for steady high-lift predictions, the 30P30N configurations has provided a valuable opportunity for the airframe noise community to collectively assess and advance the computational and experimental techniques for slat noise. The contributed solutions are compared with each other as well as with the initial measurements that became available just prior to the BANC-III Workshop. Specific features of a number of computational solutions on the finer grids compare reasonably well with the initial measurements from FSU and JAXA facilities and/or with each other. However, no single solution (or a subset of solutions) could be identified as clearly superior to the remaining solutions. Grid sensitivity studies presented by multiple BANC-III participants demonstrated a relatively consistent trend of reduced surface pressure fluctuations, higher levels of turbulent kinetic energy in the flow, and lower levels of both narrow band peaks and the broadband component of unsteady pressure spectra in the nearfield and farfield. The lessons learned from the BANC-III contributions have been used to identify improvements to the problem statement for future Category-7 investigations.

We present work towards a parameter-free method for turbulent flow simulation based on adaptive finite element approximation of the Navier-Stokes equations at high Reynolds numbers. In this model, viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimised based on solution features, in particular no bounder layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated. 

We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall-layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations.

We present a time-resolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW-2 workshop, where this method is used to compute the flow past a DLR-F11 aircraft model at realistic Reynolds number. The mesh is automatically constructed by the method as part of the computation, and no explicit turbulence model is needed. The effect of unresolved turbulent boundary layers is modeled by a simple parametrization of the wall shear stress in terms of the skin friction. In the extreme case of very high Reynolds numbers we approximate the small skin friction by zero skin friction, corresponding to a free slip boundary condition, which results in a computational model without any model parameter that needs tuning. Thus, the simulation methodology by- passes the main challenges posed by high Reynolds number CFD: the design of an optimal computational mesh, turbulence (or subgrid) modeling, and the cost of boundary layer res- olution. The results from HiLiftPW-2 presented in this report show good agreement with experimental data for a range of different angles of attack, while using orders of magnitude fewer degrees of freedom than what is needed in state of the art methods such as RANS. 

As a step toward building a more complete model of voice production mechanics, we assess the feasibility of a fluid-structure simulation of the vocal fold mechanics in the Unicorn incompressible Unified Continuum framework. The Unicorn framework consists of conservation equations for mass and momentum, a phase function selecting solid or fluid constitutive laws, a convection equation for the phase function and moving mesh methods for tracking the interface, and discretization through an adaptive stabilized finite element method. The framework has been validated for turbulent flow for both low and high Reynolds numbers and has the following features: implicit turbulence modeling (turbulent dissipation only occurs through numerical stabilization), goal-oriented mesh adaptivity, strong, implicit fluid-structure coupling and good scaling on massively parallel computers. We have applied the framework for turbulent fluid-structure interaction simulation of vocal folds, and present initial results. Acoustic quantities have been extracted from the framework in the setting of an investigation of a configuration approximating an exhaust system with turbulent flow around a flexible triangular steel plate in a circular duct. We present some results of the investigation as well as results of the framework applied to other problems.

This is a summary of preliminary results from simulations with the 30P30N high-lift device. We used the General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh is adaptively refined with respect to a posteriori error estimates for a quantity of interest. The mesh is fully unstructured and the solutions are time-resolved, which are key ingredients for solving challenging industrial applications in the field of aeroacoustics. We present preliminary results containing time-averaged quantities and snapshots of unsteady quantities, all reasonably agreeing with previous computational efforts. One important finding is that the use of adaptively generated meshes seems to be a more effcient way of computing aeroacoustic sources than by using "handmade" meshes.