Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Evaluation of major feed resources in crop-livestock mixed farming systems, southern Ethiopia: Indigenous knowledge versus laboratory analysis results

Evaluation of major feed resources was conducted in four crop-livestock mixed farming systems of central southern Ethiopia, with 90 farmers, selected using multi-stage purposive and random sampling methods. Discussions were held with focused groups and key informants for vernacular name identification of feed, followed by feed sampling to analyse chemical composition (CP, ADF and NDF), in-vitro dry matter digestibility (IVDMD), and correlate with indigenous technical knowledge (ITK). Native pastures, crop residues (CR) and multi-purpose trees (MPT) are the major feed resources, demonstrated great variations in seasonality, chemical composition and IVDMD. The average CP, NDF and IVDMD values for grasses were 83.8 (ranged: 62.9–190), 619 (ranged: 357–877) and 572 (ranged: 317–743) g kg^(−1) DM, respectively. Likewise, the average CP, NDF and IVDMD for CR were 58 (ranged: 20–90), 760 (ranged: 340–931) and 461 (ranged: 285–637)g kg^(−1) DM, respectively. Generally, the MPT and non-conventional feeds (NCF, Ensete ventricosum and Ipomoea batatas) possessed higher CP (ranged: 155–164 g kg^(−1) DM) and IVDMD values (611–657 g kg^(−1) DM) while lower NDF (331–387 g kg^(−1) DM) and ADF (321–344 g kg^(−1) DM) values. The MPT and NCF were ranked as the best nutritious feeds by ITK while crop residues were the least. This study indicates that there are remarkable variations within and among forage resources in terms of chemical composition. There were also complementarities between ITK and feed laboratory results, and thus the ITK need to be taken into consideration in evaluation of local feed resources.