The goal of this paper is to present a versatile framework for solution verification of PDE＇s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that construc...The goal of this paper is to present a versatile framework for solution verification of PDE＇s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W. Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are separately an incompressible back step flow test case and a heat transfer problem for a battery. Our error estimate might be ultimately verified with a near by manufactured solution. While our pro- cedure is systematic and requires numerous computation of residuals, one can take advantage of distributed computing to get quickly the error estimate.展开更多
Soil capacity to support life and to produce economic goods and services is strongly linked to the maintenance of good soil physical quality(SPQ). In this study, the SPQ of citrus orchards was assessed under three dif...Soil capacity to support life and to produce economic goods and services is strongly linked to the maintenance of good soil physical quality(SPQ). In this study, the SPQ of citrus orchards was assessed under three different soil managements, namely no-tillage using herbicides, tillage under chemical farming, and no-tillage under organic farming. Commonly used indicators, such as soil bulk density,organic carbon content, and structural stability index, were considered in conjunction with capacitive indicators estimated by the Beerkan estimation of soil transfer parameter(BEST) method. The measurements taken at the L'Alcoleja Experimental Station in Spain yielded optimal values for soil bulk density and organic carbon content in 100% and 70% of cases for organic farming. The values of structural stability index indicated that the soil was stable in 90% of cases. Differences between the soil management practices were particularly clear in terms of plant-available water capacity and saturated hydraulic conductivity. Under organic farming, the soil had the greatest ability to store and provide water to plant roots, and to quickly drain excess water and facilitate root proliferation.Management practices adopted under organic farming(such as vegetation cover between the trees, chipping after pruning, and spreading the chips on the soil surface) improved the SPQ. Conversely, the conventional management strategies unequivocally led to soil degradation owing to the loss of organic matter, soil compaction, and reduced structural stability. The results in this study show that organic farming has a clear positive impact on the SPQ, suggesting that tillage and herbicide treatments should be avoided.展开更多
基金Sandia Nat.Lab.Sandia is a multiprogram laboratory operated by Sandia Corporation,a Lockheed Martin Company,for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000
文摘The goal of this paper is to present a versatile framework for solution verification of PDE＇s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W. Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are separately an incompressible back step flow test case and a heat transfer problem for a battery. Our error estimate might be ultimately verified with a near by manufactured solution. While our pro- cedure is systematic and requires numerous computation of residuals, one can take advantage of distributed computing to get quickly the error estimate.
基金supported by the RECARE Project from the European Union Seventh Framework Programme (FP7/2007-2013) (No. 603498)COST actions 1306
文摘Soil capacity to support life and to produce economic goods and services is strongly linked to the maintenance of good soil physical quality(SPQ). In this study, the SPQ of citrus orchards was assessed under three different soil managements, namely no-tillage using herbicides, tillage under chemical farming, and no-tillage under organic farming. Commonly used indicators, such as soil bulk density,organic carbon content, and structural stability index, were considered in conjunction with capacitive indicators estimated by the Beerkan estimation of soil transfer parameter(BEST) method. The measurements taken at the L'Alcoleja Experimental Station in Spain yielded optimal values for soil bulk density and organic carbon content in 100% and 70% of cases for organic farming. The values of structural stability index indicated that the soil was stable in 90% of cases. Differences between the soil management practices were particularly clear in terms of plant-available water capacity and saturated hydraulic conductivity. Under organic farming, the soil had the greatest ability to store and provide water to plant roots, and to quickly drain excess water and facilitate root proliferation.Management practices adopted under organic farming(such as vegetation cover between the trees, chipping after pruning, and spreading the chips on the soil surface) improved the SPQ. Conversely, the conventional management strategies unequivocally led to soil degradation owing to the loss of organic matter, soil compaction, and reduced structural stability. The results in this study show that organic farming has a clear positive impact on the SPQ, suggesting that tillage and herbicide treatments should be avoided.
