Energy distributions of high-frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibroacoustics, seismology, electromagnetics and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or in molecular dynamics simulations. Solutions to these flow equations are often large-scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics, determining the vibroacoustic response of a cast aluminium car body component, is presented.

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energy analysis (SEA) towards non-diffusive wave fields. DEA takes into account the full directionality of the wave field and makes sub-structuring obsolete. It can thus be implemented on mesh grids commonly used, for example, in the finite element method (FEM). The resulting mesh based formulation of DEA can be implemented very efficiently using discrete flow mapping (DFM) as detailed in [1] and described here for applications in vibro-acoustics. A mid-to-high frequency vibro-acoustic response can be obtained over the whole modelled structure. Abrupt changes of material parameter at interfaces are described in terms of reflection/transmission ma- systems are considered: a double-hull structure used in the ship-building industry and a cast aluminium shock tower from a Range Rover. We demonstrate that DEA with DFM implementation can handle multi-mode wave propagation effectively, taking into account mode conversion between shear, pressure and bending waves at interfaces, and on curved surfaces.

Abstract. The simulation of drift instabilities in the plasma edge leads to cubic polynomial PDE eigenvalue problems with parameter dependent coefficients. The aim is to determine the wave number which leads to the maximum growth rate of the amplitude of the wave. This requires the solution of a large number of PDE eigenvalue problems. Since we are only interested in a smooth eigenfunction corresponding to the eigenvalue with largest imaginary part, the Jacobi-Davidson method can be applied. Unfortunately, a naive implementation of this method is much too expensive for the large number of problems that have to be solved. In this paper we will present a multilevel approach for the construction of an appropriate initial search space. We will also discuss the efficient solution of the correction equation, and we will show how optimal scaling helps to accelerate the convergence.

It is demonstrated that anomalous transport at the plasma edge in tokamaks is essentially affected by poloidal inhomogeneities in the plasma temperature and density arising, e.g., by the formation of Multifaceted Asymmetric Radiation from the Edge (MARFE) at the density limit.Ionization of neutrals released from the wall elements or injected by gas puffing through special valves is an important process in fusion plasmas [1]. The generation of charged particles and the loss of electron thermal energy result in transport processes both along and perpendicular to the magnetic flux surfaces and thus determine the densities and temperatures of plasma components. In the low (L) mode of confinement in tokamaks, which is of interest for the present study, the transport across magnetic surfaces is anomalously large compared to the neoclassical transport expected in quiet plasmas without instabilities [2]. Nowadays it is believed that the transport anomaly at the plasma edge is due to the development of drift-Alfven (DA) [3] and drift resistive ballooning (DRB) [4] instabilities, which are driven by Coulomb collisions between charged particles and inhomogeneity of the magnetic field in toroidal devices. These modes are usually analyzed under the assumption that the plasma parameters are constant on magnetic surfaces. Such an approach is justified by the fact that transport processes along the magnetic field lines are generally very fast and the plasma parameters remain nearly homogeneous on magnetic surfaces even if the particle source and associated energy loss are strongly localized. Under certain conditions, however, this assumption is not satisfied. For instance, if the density is ramped up to the Greenwald limit [5] and a plasma belt of very high density and low temperature, the so called Multifaceted Asymmetric Radiation from the Edge (MARFE), arises at the high field side (HFS) [6]. This leads to a strong poloidal variation in the plasma parameters. As it has been demonstrated before [7,8] an interplay between DA and DRB driven types of turbulence can be decisive for density limit phenomena.In this paper, we consider situations where the neutral particle sources are symmetric in the toroidal direction but strongly inhomogeneous in the poloidal one. Under the L-mode conditions, anomalous perpendicular losses of charged particles are assumed to be driven by DA and DRB micro-instabilities. In order to determine radial fluxes the fluid equations for particle and momentum transfer, the Maxwell equations, and the quasi-neutrality condition are linearized with respect to small perturbations of the densities of charged particles, radial and parallel electric currents, and electric and magnetic fields. These equations are reduced to a second order ordinary differential eigenvalue equation for the poloidal variation of the perturbation eigenfunctions, with coefficients essentially dependend on the equilibrium plasma density and temperature. The eigenvalue is related to the complex frequency of the perturbations [9]. In order...

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