A bounded upwinding scheme for computing convection-dominated transport problems

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time, and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space. While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes, vast areas of the tropics remain understudied. In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity, but it remains among the least known forests in America and is often underrepresented in biodiversity databases. To worsen this situation, human-induced modifications may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge, it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

This article deals with the study of the development and application of the high-order upwind ADBQUICKEST scheme, an adaptative bounded version of the QUICKEST for unsteady problems (Commun. Numer. Meth. Engng 2007; 23:419-445), employing both linear and nonlinear convection term discretization. This scheme is applicable to a wide range of computational fluid dynamics problems, where transport phenomena are of special importance. In particular, the performance of the scheme is assessed through an extensive numerical simulation study of advection-diffusion problems. The scheme, implemented in the context of finite difference methodology, combines a good approximation of shocks (or discontinuities) with a good approximation of the smooth parts of the solutions. In order to assess the performance of the scheme, seven problems are solved, namely (a) advection of scalars; (b) non-linear viscous Burgers equation; (c) Euler equations of gas dynamics; (d) Newtonian flow in a channel; (e) axisymmetric Newtonian jet flow; (f) axisymmetric non-Newtonian (generalized Newtonian) flow in a pipe; and (g) collapse of a fluid column. The numerical experiments clearly show that the scheme provides more consistent solutions than those found in the literature. From the study, the flexibility and robustness of the ADBQUICKEST scheme is confirmed by demonstrating its capability to solve a variety of linear and nonlinear problems with and without discontinuous solutions