Notes on numerical fluid mechanics

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.

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NURBS-enhanced finite element method (NEFEM)

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NURBS-Enhanced Finite Element Method (NEFEM)

https://www.brown.edu/research/projects/scientific-computing/sites/brown.edu.research.projects.scientific-computing/files/uploads/High%20order%20WENO%20and%20DG%20methods%20for%20time-dependent%20convection-dominated%20PDEs.pdf

High order WENO and DG methods for time-dependent convection-dominated PDEs

The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

The Boundary Element Method in Acoustics: A Survey

A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows

Source-time dominant aeroacoustics

This paper presents a method to improve the tip vortex conservation in a computational fluid dynamics simulation of a helicopter main rotor. Our approach uses vortex-adapted Chimera child grids to achieve a local refinement of the grid in the vicinity of the vortex and thus reduce the numerical dissipation of the vortex. The method is applied to the higher-harmonic-control aeroacoustic rotor test case to evaluate its potential with respect to the prediction of blade-vortex interaction airloads. To allow a meaningful comparison with the experimental data, the rotor is trimmed for thrust, as well as for longitudinal and lateral mast moments, using weak fluid-structure coupling with a flight mechanics code. We obtained a good overall agreement with the experimental data for both aerodynamics and blade dynamics. The effect of the improvement in tip vortex conservation is demonstrated by comparison with simulations without Chimera refinement and with the experimental results. It turned out that a very fine grid resolution in the vicinity of the vortex is necessary to capture the blade-vortex interaction airloads. The required grid resolution was provided by a refinement of the vortex-adapted grids, allowing for a very good reproduction of the blade-vortex interaction airloads, especially on the retreating blade side.

Tip Vortex Conservation on a Helicopter Main Rotor Using Vortex-Adapted Chimera Grids

A Parallel Discontinuous Galerkin Code for the Navier-Stokes Equations

This study intends to proof the capability of URANS computations to simulate the helicopter flight in the ground effect flow regime. Hover as well as forward flight cases are computed and compared to experimental data. For both flight conditions several parameter variations, such as ground distance, collective pitch and normalized advance ratio, were examined. Overall a good representation of the flow field structure could be obtained, as well as a satisfying approximation for the thrust coefficient. Furthermore, conclusions could be drawn regarding unsteady effects in the wake and their influence on the brown-out phenomenon. Especially the dynamic fluid movement around the Flow Separation Point is a considerable source of unsteadiness and energy introduced in the brown-out particle movement.

Manuel Kessler

Papers

A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows

Source-time dominant aeroacoustics

Tip Vortex Conservation on a Helicopter Main Rotor Using Vortex-Adapted Chimera Grids

A Parallel Discontinuous Galerkin Code for the Navier-Stokes Equations

Numerical investigation of helicopter rotors in ground effect