Catálogo de publicaciones - libros

We investigate the interaction of shock waves in a heavy gas with embedded light gas bubbles next to a rigid wall. This may give insight regarding cavitation processes in water. Due to the highly dynamical, unsteady processes under consideration we use an adaptive FV scheme for the computations to resolve accurately all physically relevant effects. The results are validated by comparison with tube experiments.

A finite volume method has been developed in this work for solving the conservation equations of argon plasma flows in magnetoplasmadynamic self-field accelerators. These accelerators can be used for interplanetary spaceflight missions because of their high specific impulse and high thrust density.

Calculations show in agreement with the experiment that a primary reason for plasma instabilities at high current settings — which are limiting the operational envelope and the thruster lifetime — is the depletion of density and charge carriers in front of the anode because of the pinch effect.

The calculated thrust data agree well with experimental values, so that the newly developed method can be used for the design and optimization of new thrusters.

The paper deals with the transition regime of gas flows between the mesoscopic and the macroscopic levels. We survey theoretical results and provide numerical tools. As the basic numerical scheme for the solution of the Boltzmann equation we use a hexagonal model proposed in [1].

Numerical simulations can be the key to the thorough understanding of the multi-dimensional nature of transient detonation waves. But the accurate approximation of realistic detonations is extremely demanding, because a wide range of different scales need to be resolved. This paper describes an entire solution strategy for the Euler equations of thermally perfect gas-mixtures with detailed chemical kinetics that is based on a highly adaptive finite volume method for blockstructured Cartesian meshes. Large-scale simulations of unstable detonation structures of hydrogen-oxygen detonations demonstrate the efficiency of the approach in practice.

The Rayleigh-Bénard problem and the Taylor-Couette problem are two well-known stability problems that are traditionally treated with linear stability analysis. In the vast majority of these stability calculations the fluid is considered to be incompressible [Cha61, DR81]. Only with this assumption and simplification is possible to conduct a linear stability analysis analytically.

In order to calculate the stability limits of a compressible fluid by use of a linear stability analysis therefore in this work a numerical linear stability analysis is presented. The numerical stability analysis is based upon the equations of balance for mass, momentum and energy that are completed with the constitutive equations by Navier-Stokes and Fourier. The algorithm allows to calculate the regions of stability for arbitrary one-dimensional and stationary basic states.

This numerical stability analysis is used to calculate the stability region for the Rayleigh-Bénard problem. The main result is that the critical Rayleigh number does not have a constant value, as calculations involving the Boussinesq approximation suggest misleadingly, but that the value of the critical Rayleigh number depends strongly on the thickness of the fluid layer. Furthermore, an empirically found relationship between the critical Rayleigh number and the thickness of the fluid layer is presented (14). Its efficiency is successfully verified with the results of the numerical linear stability analysis. The results for the critical Rayleigh number show clearly that the compressibility of a fluid must not be neglected in the stability analysis of the Rayleigh-Bénard problem.

Secondly, the more complicated Taylor-Couette problem is treated with the numerical linear stability analysis. In contrast to the traditional stability analysis by Taylor [Tay23], the fluid is considered to be compressible and includes the temperature as a field variable. The effectiveness of the numerical linear stability analysis is manifested by the good agreement of the comparison with experimental results. In addition to that, temperature effects are studied and are compared with experiments.

This paper proposes a general multi-dimensional front tracking concept for various physical problems involving specially discontinuous solution features. The tracking method is based on the level-set approach with a restricted dynamic definition range in the vicinity of the fronts on fixed grids of arbitrary cell structure.

To combine the front tracking procedure with the continuous part of the field to be simulated, a double sided flux discretization called flux-separation and a set of inner boundary conditions over the discontinuities are used. The methods developed are not restricted to fluid dynamics, however all examples relate to this class of simulation problems.

Special attention is drawn to the restrictions of the classical level-set method, i.e. accuracy issues and topological restrictions. In this concern, an improved time integration method for the front motion is introduced and the problem of interacting discontinuities is addressed. The methods are integrated in the object oriented Finite-Volume solution package MOUSE [1] for systems of conservation laws on arbitrary grids.

An exact Riemann solver is developed for the investigation of non-classical wave phenomena in BZT fluids and fluids which undergo a phase transition. Here we outline the basic construction principles of this Riemann solver employing a general equation of state that takes negative nonlinearity and phase transition into account. This exact Riemann solver is a useful validation tool for numerical schemes, in particular, when applied to the aforementioned fluids. As an application, we present some numerical results where we consider flow fields exhibiting non-classical wave phenomena due to BZT fluids and phase transition.

The equations of compressible radiation magnetohydrodynamics provide a widely accepted mathematical model for the basic fluid-dynamical processes in the sun's atmosphere. From the mathematical point of view the equations constitute an instance of a system of non-local hyperbolic balance laws. We have developed and implemented numerical methods in three space dimensions on the basis of a finite volume scheme that allow the efficient approximation of weak solutions. Key features are the use of efficient Riemann solvers, a special treatment of the divergence constraint, higher-order schemes, the extended short characteristics method, local mesh adaption, and parallelization using dynamic load balancing. Moreover, methods to cope with the special nature of the atmosphere are included.

In this contribution we give an overview of our work, highlight our most important results, and report on some new developments. In particular, we present a scalar model problem for which an almost complete analytical treatment is possible.

The hyperbolic system that describes heat conduction at low temperatures and the relativistic Euler equations belong to a class of hyperbolic conservation laws that result from an underlying kinetic equation. The focus of this study is the establishment of an kinetic approach in order to solve initial and boundary value problems for the two examples. The ingredients of the kinetic approach are: (i) Representation of macroscopic fields by moment integrals of the kinetic phase density. (ii) Decomposition of the evolution into periods of free flight, which are interrupted by update times. (iii) At the update times the data are refreshed by the Maximum Entropy Principle.

This paper proposes a general multi-dimensional front tracking concept for various physical problems involving specially discontinuous solution features. The tracking method is based on the level-set approach with a restricted dynamic definition range in the vicinity of the fronts on fixed grids of arbitrary cell structure.

To combine the front tracking procedure with the continuous part of the field to be simulated, a double sided flux discretization called flux-separation and a set of inner boundary conditions over the discontinuities are used. The methods developed are not restricted to fluid dynamics, however all examples relate to this class of simulation problems.

Special attention is drawn to the restrictions of the classical level-set method, i.e. accuracy issues and topological restrictions. In this concern, an improved time integration method for the front motion is introduced and the problem of interacting discontinuities is addressed. The methods are integrated in the object oriented Finite-Volume solution package MOUSE [1] for systems of conservation laws on arbitrary grids.