Stability of preconditioned finite volume schemes at low Mach numbers

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an explicit time integration scheme turns out to be unstable if the time step Dt does not satisfy the requirement to be O(M2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Dt=O(M), M to 0, which results from the well-known CFL-condition. We present a comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. Thereby, we present statements for both the standard preconditioner used by Guillard and Viozat [4] and the more general one due to Turkel [21]. The theoretical results are after wards confirmed by numerical experiments.

Numerical simulation of tunnel fires using preconditioned finite volume schemes

This article is concerned with the numerical simulation of flows at low Mach numbers which are subject to the gravitational force and strong heat sources. As a specific example for such flows, a fire event in a car tunnel will be considered in detail. The low Mach flow is treated with a preconditioning technique allowing the computation of unsteady flows, while the source terms for gravitation and heat are incorporated via operator splitting. It is shown that a first order discretization in space is not able to compute the buoyancy forces properly on reasonable grids. The feasibility of the method is demonstrated on several test cases.

Labelling schemes for organic food: Consumer attitudes, preferences and willingness-to-pay in six European countries

Since July 2010, all pre-packed organic food produced in the European Union (EU) must carry the new mandatory EU logo for organic food. Voluntary organic labels (such as national governmental logos and logos of private farmers’ associations and control bodies) can still be used, but only in addition to the mandatory EU logo. This change in the regulatory environment of organic labelling raises a number of questions regarding consumer preferences for different kinds of organic certification logos, which the present dissertation addressed. The first objective was to explore and analyse consumer perceptions, attitudes, preferences and willingness-to-pay (WTP) regarding different voluntary organic labels. The second objective was to investigate consumer perceptions and attitudes towards a mandatory EU logo. A combination of qualitative and quantitative methods of consumer research in six European countries was employed including focus group discussions, choice experiments and structured interviews. Based on the empirical results, recommendations are drawn for different actors in the organic sector.

Transaction costs of farmers’ participation in forest management: Policy implications of payments for environmental services schemes in Vietnam

Recent research on payments for environmental services (PES) has observed that high transaction costs (TCs) are incurred through the implementation of PES schemes and farmer participation. TCs incurred by households are considered to be an obstacle to the participation in and efficiency of PES policies. This study aims to understand transactions related to previous forest plantation programmes and to estimate the actual TCs incurred by farmers who participated in these programmes in a mountainous area of northwestern Vietnam. In addition, this study examines determinants of households’ TCs to test the hypothesis of whether the amount of TCs varies according to household characteristics. Results show that average TCs are not likely to be a constraint for participation since they are about 200,000 VND (USD 10) per household per contract, which is equivalent to one person’s average earnings for about two days of labour. However, TCs amount to more than one-third of the programmes’ benefits, which is relatively high compared to PES programmes in developed countries. This implies that rather than aiming to reduce TCs, an appropriate agenda for policy improvement is to balance the level of TCs with PES programme benefits to enhance the overall attractiveness of afforestation programmes for smallholder farmers. Regression analysis reveals that education, gender and perception towards PES programmes have significant effects on the magnitude of TCs. The analyses also points out the importance of local conditions on the level of TCs, with some unexpected results.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.