Catálogo de publicaciones - libros

Some years ago the national CFD project MEGAFLOW was initiated in Germany, which combined many of the CFD development activities from DLR, universities and aircraft industry. Its goal was the development and validation of a dependable and efficient numerical tool for the aerodynamic simulation of complete aircraft which met the requirements of industrial implementations. The MEGAFLOW software system includes the block-structured Navier-Stokes code FLOWer and the unstructured Navier-Stokes code TAU. Both codes have reached a high level of maturity and they are intensively used by DLR and the German aerospace industry in the design process of new aircraft. Recently, the follow-on project MEGADESIGN was set up which focuses on the development and enhancement of efficient numerical methods for shape design and optimization. This paper highlights recent improvements and enhancements of the software. Its capability to predict viscous flows around complex industrial applications for transport aircraft design is demonstrated. First results concerning shape optimization are presented.

The optimal profile of turbine blades is crucial for the efficiency of modern powerplants. The applied SQP algorithms are based on gradient information.

In this work I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of the work was implementation and test of a method for interpolation of 3D points by regular parametric curves, and fast and efficient evaluation of these functions for a good resolution of rendering. For this purpose I have used a parallel environment using a multiprocessor cluster architecture. The efficiency of the used method is good, mainly reducing the number of floating-points computations by caching the numerical values of some line-parameter’s powers, and reducing the necessity of communication among processes. This work has been developed for the Research & Development Department of my company for planning advanced customized models of industrial burners.

Optimal path-constrained trajectories of an ISS-based, three-link robot are investigated with a monorail as an additional fourth and prismatic joint. This results in a problem of optimal control for a multiple constrained nonlinear system of differential-algebraic equations. After transformation into minimum coordinates, the only remaining control is the acceleration of the end-effector along the prescribed trajectory, replacing four actuator torques/forces in the original formulation. The simpler structure is achieved at the price of introducing piecewise defined equations of motion, two highly nonlinear control constraints and two state constraints of first order. Switching points between partly linear and fully rotational motion are optimized. Solutions are presented including touch points of the state constraints with the two control constraints being active simultaneously. For the mathematical treatment of those problems, new interior point conditions are derived.

The transmitting spherical reflector antenna (SRA) has a well-known rigorous solution form as a second kind Fredholm system that is well conditioned when truncated to a finite system. The size of such systems for extremely large SRAs require specially designed highly efficient numerical algorithms to make their analysis feasible. Two significant features of the system are that its convolution format admits a computationally rapid implementation of the bi-conjugate gradient method, and at high frequencies, a certain decoupling occurs. These features allow an effective numerical treatment of apertures some thousands of wavelengths.

This paper describes the present status of using lattice gauge and ghost field methods for the simulation of on-chip interconnects and integrated passive components at low and high frequencies. Test structures have been developed and characterized in order to confront the simulation techniques with experimental data. The solution method gives results that are in agreement with the measurements.

Surface acoustic wave filters are widely used for frequency filtering in telecommunications. These devices mainly consist of a piezoelectric substrate with periodically arranged electrodes on the surface. The periodic structure of the electrodes subdivides the frequency domain into stop-bands and pass-bands. This means only piezoelectric waves excited at frequencies belonging to the pass-band-region can pass the devices undamped.

The goal of the presented work is the numerical calculation of so-called “dispersion diagrams”, the relation between excitation frequency and a complex propagation parameter. The latter describes damping factor and phase shift per electrode.

The mathematical model is governed by two main issues, the underlying periodic structure and the indefinite coupled field problem due to piezoelectric material equations. Applying Bloch-Floquet theory for infinite periodic geometries yields a unit-cell problem with quasi-periodic boundary conditions. We present two formulations for a frequency-dependent eigenvalue problem describing the dispersion relation.

Reducing the unit-cell problem only to unknowns on the periodic boundary results in a small-sized quadratic eigenvalue problem which is solved by QZ-methods. The second method leads to a large-scaled generalized non-hermitian eigenvalue problem which is solved by Arnoldi methods.

The effect of periodic perturbations in the underlying geometry is confirmed by numerical experiments. Moreover, we present simulations of high frequency SAW- filter structures as used in TV-sets and mobile phones.

Diffraction gratings are often used in optical metrology. When an electromagnetic wave is incident on a grating, the periodicity of the grating causes a multiplicity of diffraction orders. In many metrology applications one needs to know the diffraction efficiency of these orders. Since the period of a grating is often of the same order of magnitude as the wavelength, it is needed to solve Maxwell’s equations rigorously in order to obtain these diffraction efficiencies. Two of those methods are the rigorous coupled-wave analysis (RCWA) and the C method.

In this paper a comparison is made between RCWA and the C method with respect to accuracy and speed. Restrictions are made to one-interface problems, which means that only two media are involved separated by one interface, and only gratings are considered with a periodicity in only one direction.

A numerical study of domain wall relocation during slow voltage switching is presented for doped semiconductor superlattices. Unusual relocation scenarios are found and interpreted according to previous theory.

A nonlocal (quantum) drift-diffusion equation for the electric field and the electron density is derived from a Wigner-Poisson equation modelling quantum vertical transport in strongly coupled semiconductor superlattices, by using a consistent Chapman-Enskog procedure. Numerical solutions for a device consisting of a n-doped superlattice placed in a -- diode under a constant voltage bias are presented and compared with those obtained by using a semiclassical approximation.