Random Diophantine inequalities of additive type

Using the Davenport–Heilbronn circle method, we show that for almost all additive Diophantine inequalities of degree k in more than 2k variables the expected asymptotic formula for the density of solutions holds true.     

Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media

This article presents a new nonlinear finite‐volume scheme for the nonisothermal two‐phase two‐component flow equations in porous media. The face fluxes are approximated by a nonlinear two‐point flux approximation, where transmissibilities nonlinearly depend on primary variables. Thereby, we mainly follow the ideas proposed by Le Potier combined with a harmonic averaging point interpolation strategy for the approximation of arbitrary heterogeneous permeability fields on polygonal grids. The behavior of this interpolation strategy is analyzed, and its limitation for highly anisotropic permeability tensors is demonstrated. Moreover, the condition numbers of occurring matrices are compared with linear finite‐volume schemes. Additionally, the convergence behavior of iterative solvers is investigated. Finally, it is shown that the nonlinear scheme is more efficient than its linear counterpart. Copyright © 2016 John Wiley & Sons, Ltd.     

High-repetition-rate PIV investigations on a generic rocket model in sub- and supersonic flows

High-repetition-rate PIV measurements were performed in the trisonic wind tunnel facility at the Bundeswehr University Munich in order to investigate the boundary layer parameters on a generic rocket model and the recirculation area in the wake of the model at Mach numbers up to Mach = 2.6. The data are required for the validation of unsteady flow simulations. Because of the limited run time of the blow-down wind tunnel, a high-repetition-rate PIV system was applied to obtain the flow statistics with high accuracy. The results demonstrate this method’s potential to resolve small-scale flow phenomena over a wide field of view in a large Mach number range but also show its limitations for the investigations of wall-bounded flows.