Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.Comment: 19 pages, 7 figure

Investigation of the Properties of Galactic Cosmic Rays with the KASCADE-Grande Experiment

The properties of galactic cosmic rays are investigated with the KASCADE-Grande experiment in the energy range between $10^{14}$ and $10^{18}$ eV. Recent results are discussed. They concern mainly the all-particle energy spectrum and the elemental composition of cosmic rays.Comment: Proc. RICAP 09, Nucl. Instr. and Meth. in pres

The spectrum of high-energy cosmic rays measured with KASCADE-Grande

The energy spectrum of cosmic rays between 10**16 eV and 10**18 eV, derived from measurements of the shower size (total number of charged particles) and the total muon number of extensive air showers by the KASCADE-Grande experiment, is described. The resulting all-particle energy spectrum exhibits strong hints for a hardening of the spectrum at approximately 2x10**16 eV and a significant steepening at c. 8x10**16 eV. These observations challenge the view that the spectrum is a single power law between knee and ankle. Possible scenarios generating such features are discussed in terms of astrophysical processes that may explain the transition region from galactic to extragalactic origin of cosmic rays.Comment: accepted by Astroparticle Physics June 201

Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

We present a review of the semi-Lagrangian method for advection-diusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable

The KASCADE-Grande Experiment and the LOPES Project

KASCADE-Grande is the extension of the multi-detector setup KASCADE to cover a primary cosmic ray energy range from 100 TeV to 1 EeV. The enlarged EAS experiment provides comprehensive observations of cosmic rays in the energy region around the knee. Grande is an array of 700 x 700 sqm equipped with 37 plastic scintillator stations sensitive to measure energy deposits and arrival times of air shower particles. LOPES is a small radio antenna array to operate in conjunction with KASCADE-Grande in order to calibrate the radio emission from cosmic ray air showers. Status and capabilities of the KASCADE-Grande experiment and the LOPES project are presented.Comment: To appear in Nuclear Physics B, Proceedings Supplements, as part of the volume for the CRIS 2004, Cosmic Ray International Seminar: GZK and Surrounding

An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier-Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. We do this in the usual way away from the boundaries, by replacing the incompressibility condition on the velocity by a Poisson equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy (in L-infinity), for both the velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure

Radio Emission in Atmospheric Air Showers: First Measurements with LOPES-30

When Ultra High Energy Cosmic Rays interact with particles in the Earth's atmosphere, they produce a shower of secondary particles propagating toward the ground. LOPES-30 is an absolutely calibrated array of 30 dipole antennas investigating the radio emission from these showers in detail and clarifying if the technique is useful for largescale applications. LOPES-30 is co-located and measures in coincidence with the air shower experiment KASCADE-Grande. Status of LOPES-30 and first measurements are presented.Comment: Proceedings of ARENA 06, June 2006, University of Northumbria, U