A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS-C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non-oscillatory scheme is demonstrated by solving two-dimensional compressible flow problems, such as shock wave propagation and two-dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell-interface reconstruction technique works very well in several practical applications. (C) 2012 Elsevier Inc. All rights reserved.

Differentiability of bizonal positive definite kernels on complex spheres

We prove that any continuous function with domain {z ∈ C: |z| ≤ 1} that generates a bizonal positive definite kernel on the unit sphere in 'C POT.Q' , q ⩾ 3, is continuously differentiable in {z ∈ C: |z| < 1} up to order q − 2, with respect to both z and 'Z BARRA'. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z ∈ C: |z| < 1} up to the same order.

Photosynthetic efficiency and rate of CO2 assimilation by Arthrospira (Spirulina) platensis continuously cultivated in a tubular photobioreactor

Similar to other photosynthetic microorganisms, the cyanobacterium Arthrospira platensis can be used to produce pigments, single cell proteins, fatty acids (which can be used for bioenergy), food and feed supplements, and biofixation of CO2. Cultivation in a specifically designed tubular photobioreactor is suitable for photosynthetic biomass production, because the cultivation area can be reduced by distributing the microbial cells vertically, thus avoiding loss of ammonia and CO2. The aim of this study was to investigate the influence of light intensity and dilution rate on the photosynthetic efficiency and CO2 assimilation efficiency of A. platensis cultured in a tubular photobioreactor in a continuous process. Urea was used as a nitrogen source and CO2 as carbon source and for pH control. Steady-state conditions were achieved in most of the runs, indicating that continuous cultivation of this cyanobacterium in a tubular photobioreactor could be an interesting alternative for the large-scale fixation of CO2 to mitigate the greenhouse effect while producing high protein content biomass.