Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation

A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method. \u

Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing. \u

Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations on deforming meshes

An overview is given of a space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations. This method is well suited for problems with moving (free) boundaries which require the use of deforming elements. In addition, due to the local discretization, the space-time discontinuous Galerkin method is well suited for mesh adaptation and parallel computing. The algorithm is demonstrated with computations of the unsteady \ud ow field about a delta wing and a NACA0012 airfoil in rapid pitch up motion

Extension of the discontinuous Galerkin finite element method to viscous rotor flow simulations

Heavy vibratory loading of rotorcraft is relevant for many operational aspects of helicopters, such as the structural life span of (rotating) components, op- erational availability, the pilot’s comfort, and the ef- fectiveness of weapon targeting systems. A precise understanding of the source of these vibrational loads has important consequences in these application ar- eas. Moreover, in order to exploit the full poten- tial offered by new vibration reduction technologies, current analysis tools need to be improved with re- spect to the level of physical modeling of flow phe- nomena which contribute to the vibratory loads. In this paper, a computational fluid dynamics tool for rotorcraft simulations based on first-principles flow physics is extended to enable the simulation of vis- cous flows. Viscous effects play a significant role in the aerodynamics of helicopter rotors in high-speed flight. The new model is applied to three-dimensional vortex flow and laminar dynamic stall. The applica- tions clearly demonstrate the capability of the new model to perform on deforming and adaptive meshes. This capability is essential for rotor simulations to accomodate the blade motions and to enhance vor- tex resolution

Experimental investigation of the compressibility and permeability of fabric reinforcements : abstract

ABSTRACT: A measurement method for the out-of-plane permeability is presented in this paper. The developed permeameter is capable to measure both compression as well as the out-of-plane permeability. First results show an out-of-plane permeability that is in accordance with values found elsewhere. The compression test needs some more refinement and is not discussed here. The design of the instrument is such that it is relatively easy to change a preform between subsequent tests. A first attempt has been made to measure the viscosity of the test fluid in-line

Impact damage in woven fabric reinforced composites

Very often, woven fabrics are used as the reinforcement in advanced composite materials. Although the resulting inplane stiffness is lower than of their unidirectional counterparts, the excellent drapability of these materials eases the production of more general doubly curved components. In addition, the inherently low out-of-plane strength of these layered materials improves due to the undulating yarns. This paper considers both the initiation and growth of defects in these woven fabric reinforced plastics. Ten Cate Advanced Composites’ 5H Satin carbon reinforced PPS is taken as the model system. A 5H satin fabric exhibits very good drapability and PPS has a low viscosity above its melting point, enabling good yarn impregnation. Apart from this PPS has approved solvent resistance for aerospace applications and good temperature resistance. For a thermoplastic matrix, however, the material is fairly brittle

U.S. Antidumping Policies: The Case of Steel

This paper examines the controversy surrounding recent allegations that foreign producers are dumping steel products onto U.S. markets. The paper is in four sections, which take four quite distinct views of dumping and recent U.S. antidumping policies, emphasizing the changing definition of dumping and the development of administrative procedures. Section II focuses on the application of these procedures to the international steel trade, taking as a case study the most noteworthy of recent innovations : the Trigger Price Mechanism for steel. Section III considers models that can be used to analyze dumping. The models of most relevance to the practices currently at issue in the steel industry seem to us models of oligopolistic rivalry in imperfectly competitive, segmented markets. We develop a model designed to identify crucial factors upon which the incidence of dumping will depend: the number of firms producing for each national market,their costs, their market shares, and the extent to which they recognizeand exploit their mutual dependence. Finally, in Section IV we calibrate these models to illustrate how the extent of dumping and the effects of the TPM depend on the model's parameters.