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An object-oriented implementation in C++ of the Berger-Oliger adaptive mesh refinement algorithm for hyperbolic conservation laws is described. The software design is tailored especially for distributed memory super-computers. An examplary computation for the standard inviscid Euler equations is shown.
The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime
(2009)
AbstractIt is well known, that standard upwind schemes for the Euler equations face a number of problems in the low Mach number regime: stiffness, cancellation and accuracy problems. A new aspect, presented in this paper, is the dependence on the cell geometry: applied on a triangular grid, the accuracy problem disappears, i.e. flows of arbitrarily small Mach numbers can be simulated on a fixed mesh. We give an asymptotic analysis of this, up to date unknown, phenomenon for the first-order Roe scheme and present a number of numerical results.Keywords: Incompressible and compressible flow; Euler equations; Low Mach number flow; Roe scheme; Numerical dissipation; Asymptotic analysisPACS classification codes: 47.11.Df; 47.11.%26#8722;j; 47.15.G%26#8722;; 47.15.km
The carbuncle phenomenon, an instability of discrete shock profiles, has been known in gas dynamics simulations for a long time. Only recently, it was also observed in shallow water simulations. It was shown that the mechanisms and cures in shallow water are closely related to the mechanisms and cures in gas dynamics. In this paper, we give further evidence of that and, by means of new test cases, give evidence of the strength of our HLLEMCC approach to avoid the carbuncle in shallow water.
Although biological soil crusts can be found in open landscapes worldwide, their species composition depends on soil properties such as texture and pH, on microclimate, and their respective developmental stage. In addition, local variations in water holding capacity and/or chemical properties of soils influence the formation of spatial patterns and different types of biocrusts on the landscape level. For the evaluation of biocrusts functions and their impact on soil carbon pools, the analysis of the interrelationship between photosynthetic activity and the variations of spatial distribution pattern and types of biocrust is indispensable. For this purpose, an image processing approach was applied that combined chlorophyll fluorescence analyses and multispectral BNDVI to comprehensively characterize the spatial patterns of photosynthetic hotspots in biological soil crusts. For image analysis, five biological soil crust samples with different ratios of substrate, mosses and lichens were collected on an inland dune system in Lieberose, dominated by the moss Polytrichum piliferum, and the lichens Cladonia fimbriata and C. coccifera. RGB-images of the biocrusts were taken with a standard consumer camera Nikon 5200, BNDVI images with a modified Canon S110 NIR camera and chlorophyll fluorescence images with a modular open FluorCAM FC 800-O/1010, respectively. BNDVI and Fv/Fm were nearly in the same range for all biocrust samples related to the total surface area. Although mosses showed higher BNDVI than lichens within the separate biocrust samples. F0 and Fm increased with species coverage and with advancing biocrust development. Overlapping of BNDVI with F0 and Fm images showed that not all crustal organisms contribute to BNDVI and chlorophyll fluorescence. The overlapping areas of BNDVI and F0 ranged between 13% and 29%, that of BNDVI and Fm between 17% and 47%. Matching of RGB, BNDVI and CFI allows visualizing spatial pattern with high or low photosynthesis in biocrusts.