On the design of block preconditioners for maritime engineering

The iterative error can be an important part of the total numerical error of any Com- putational Fluid Dynamics simulation when the iterative convergence stagnates or when loose convergence criteria are used. In the quest for better iterative convergence of CFD simulations, we consider the design of iterative methods for the Reynolds-averaged Navier-Stokes equations, discretized by finite-volume methods with cell-centered, co-located variables. The central point is the approximation of the Schur complement (pressure matrix) in the block factorization of the discrete system of mass and momentum equations. We show particular approximations of these blocks that yield either segregated solvers or block preconditioners for fully coupled solvers. The performance of these solvers are then demonstrated by computing the flow over a flat plate and around a tanker on both structured and unstructured grids. We find that iterative convergence to machine precision is attainable despite the high Reynolds numbers and mesh aspect ratio’s. Improved approximations of the Schur complement do result in improved convergence rates, but do not seem to pay-off in terms of total cost compared to the basic SIMPLE-type approximation

Seasonal water balance of a sandy soil in Niger cropped with pearl millet, based on profile moisture measurements

In the Sahel, calculation of the field water balance from neutron-probe measurements is often difficult for pearl millet (Pennisetum glaucum (L.) R. Br.), which is due to the rapid drainage (D) of the sandy soils, on which it is typically grown. We present a simple method of calculating D in these soils from weekly neutron-probe data. The method divides the water balance into two phases. In the first, applicable early in the season, water flux across the maximum depth of probe measurement (Zm) is assumed negligible, and evapotranspiration (E) and D are calculated from the change in soil water content (θ) between the bottom of the rootzone (Zr) and Zm, thus allowing calculation of unsaturated hydraulic conductivity, K(θ), from the flux across Zr. In the second phase, when soil water starts to percolate across Zm, D is calculated from K(θ), assuming a hydraulic head gradient of −1. The method is used to calculate a one-dimensional water balance of a pearl-millet crop grown in a deep sandy soil at two fertility levels during a season of normal rainfall. Results show that the calculated K(θ) functions compare well with those based on laboratory measurements. An acceptable estimate of drainage, and therefore E could be made. Mean cumulative E and D were, respectively, 211 and 207 mm for the unfertilized crop, and 268 and 148 mm for the fertilized crop with 440 mm of rainfall received during the crop cycle. The fertilized millet crop water balance was simulated, which compared to the calculation method resulted in an about 10% higher seasonal E and a 10% lower seasonal D. Our study shows that E can be corrected for D using a simple but accurate method, and consistent with other studies in the region indicates that rainfall is usually not the primary limiting factor to pearl-millet productio

Low Input Technology Options for Millet-based Cropping Systems in the Sahel

Pearl millet is a staple cereal cultivated mainly by subsistence farmers on 14 million ha of the West African semi-arid tropics. Increasing pressure on the land has reduced the length of the fallow periods, which are necessary to restore soil fertility, resulting in declining yields. To investigate ways of reversing this decline, three systems combining phosphorus fertilizer application, improved varieties of millet and cowpea, and improved agronomic practices were compared with the traditional millet–cowpea intercrop system in a three year experiment. The most productive system involved the rotation of fertilized millet and cowpea. Pre-sowing tillage increased hay and fodder yields in all the improved systems. The application of fertilizer increased the amount of available phosphorus in the soil. Soil pH declined somewhat in all treatments, although the initially low soil organic matter did not change

Management Options for Intensifying Millet Based Crop Production Systems on Sandy Soils in the Sahel

Pearl millet [Pennbelum glaucum (L.) R. Br.] is a major staple crop grown on 14 millton ha ofthe semi-arid Sahellan and Sudanian ecological zones. The crop is generally grown in association with cowpea [VLgna ungulculata (L.) Walpl by subsistence fanners using manual labor for all cropping operations. Chemlcal fertilizers are rarely applled. Cash Inputs for crop husbandry are llmited to the occasional hiring of labor. Labor shortages are most severe for weeding operations. The millet-growing area in Niger has doubled to 3.2 mllllon ha during the last 25 years, while average grain yields have dropped from 0.48 Mg/ha to 0.30 Mg/ha (Anonymous, 1987). The decllne in yields suggest8 that: productlon has expanded into lncreaaingly marglnal areas, fallow periods have become too short to allow natural restoration of fertlllty, and technical change hae not yet had an impact on food productlon (Spencer, 19851. In the future, it will be necessary for production increases to come from increased yields. Experience at the ICRISAT Sahellan Center (ISC) leads us to believe yleld increases are technically feasible if the principal limitlng factors-inherently low soil fertility, limited and untlmely cultural practices, and the occurrence of drought periods-are overcome (Fussell et at.. 1987: Klaij and Hoogrnoed, 1987)

Tillage and Planting Strategies for Sandy Soils in Niger, West Africa

The Sahellan zone Is characterized by harsh conditions for crop growth: chemically and physically poor soils, low and uncertain rainfall, and high temperatures. Crops are particularly sensitive to the physical environment during the germination and seedling stages of crop establishment. Appropriate soli management techniques reduce the risk for crop failure and help to ensure good crop stands

The effect of crop residue and fertilizer use on pearl millet yields in Niger

A field study was conducted over a 4-year period in Niger, West Africa, to determine the effects of crop residue (CR), fertilizer, or a combination of crop residue and fertilizer(CRF) on yields of pearl millet(Pennisetum glaucum[L.] R.Br.). Despite a decline in yields of control plots (initial yields were 280kg grain ha-1 declining to 75 kg grain ha - 1 over 4 years), yield of fertilizer plots were maintained at 800-1,000 kg grain ha-1. Continued application of CR slowly augmented yields to levels similar to those of the fertilized plots. The effects of CR and fertilizer were approximately additive in the CRF plots. Addition of CR and fertilizer increased soil water use over the control by 57 mm to 268 mm in an average season and helped trap wind-blown soil. These plots tended to exhibit slightly higer soil pH and lower A1 saturation than did the fertilized treatments. Return of CR to the soil resulted in significantly reduced export of most plant nutrients, especially Ca, Mg, and

Infiltration, runoff and drainage in the Sudano-Sahelian zone

We present a brief overview of methods suitable for measuring or estimating infiltration. runoff or drainage. Since an exhaustive mrvior is not fcaaibie in the context of this paper, the emphasis h on field methods which are not too complicated or expensive, and suitable for use in the Sudano Sahelian zone. Methods for measurements over large areas, e.& catchments. are not included. Obviously, for natural events where interception of rainfall by the vegetation can be ignored. Idbation and runoff together equal precipitation: onh. two of the three procuacs need be quantified to quantib the other. For each method a brief dewription is given, together with a suitable reference for further information

Tillage systems and soils in the semi-arid tropics

Even though conservation tillage may be ideal for the semi-arid tropics (SAT) in view of results from studies and tillage practices in the U.S.A. and Australia, studies conducted in semi-arid regions of Africa appear to support the use of conventional tillage systems. Some of the reasons for this apparent discrepancy are because of the physical properties of the soils in semi-arid Africa, particularly the Sahelian zones where the soils are sandy, have high bulk densities and therefore low total porosities and form crusts upon wetting and drying. Consequently, no-till or reduced tillage systems that do not have the soil surface covered by residue in irder to prevent formation of crust as a result of raindrop impact, tend to lose water through runoff in a region where water economy is essential. Also, because these soils have inherently high bulk densities, conventional tillage systems appear to be suitable since they increase the macropores, reduce both bulk density and strength and thus ensure prolific root distribution and the resultant exploration of water and nutrients at greater soil depths. Notwithstanding, it seems that since most of the SAT soils are structurally unstable, further conventional tillage even though it has ephemeral advantages, may in the long term be exacerbating the problems of structural instability and their deleterious effect on water and soil conservation and therefore on crop production. We suggest that at this stage soil tillage research in the semi-arid regions of Africa and Asia should re-examine some of the concepts of conservation tillage in relation to soil physical properties and processes in order to obtain a tillage system that ensures high crop yields without destruction of the soil resource

Management Practices to Increase Yield and Yield Stability of Pearl Millet in Africa

Fertility, soil, and crop management practices that could have an impact on improving millet production in the major millet growing areas of Africa are described. These factors are examined in terms of their potential impact on production and their availability to the resource-poor farmer. Important practices that optimize the use of available water are discussed. If farmers of the semi-arid tropics of West Africa1190improve the fertility of their soils and move from hand tools to using animal traction, increased and stable yields are possible in this drought-prone region