A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Effects of chlorogenic acid and bovine serum albumin on the oxidative stability of low density lipoproteins in vitro

The ability of chlorogenic acid to inhibit oxidation of human low-density lipoprotein (LDL) was studied by in vitro copper-induced LDL oxidation. The effect of chlorogenic acid on the lag time before LDL oxidation increased in a dose dependent manner by up to 176% of the control value when added at concentrations of 0.25 -1.0 μM. Dose dependent increases in lag time of LDL oxidation were also observed, but at much higher concentrations, when chlorogenic acid was incubated with LDL (up to 29.7% increase in lag phase for 10 μM chlorogenic acid) or plasma (up to 16.6% increase in lag phase for 200 μM chlorogenic acid) prior to isolation of LDL, and this indicated that chlorogenic acid was able to bind, at least weakly, to LDL. Bovine serum albumin (BSA) increased the oxidative stability of LDL in the presence of chlorogenic acid. Fluorescence spectroscopy showed that chlorogenic acid binds to BSA with a binding constant of 3.88 x 104 M-1. BSA increased the antioxidant effect of chlorogenic acid, and this was attributed to copper ions binding to BSA, thereby reducing the amount of copper available for inducing lipid peroxidation.

Enhancing the oxidative stability of rice crackers by addition of the ethanolic extract of phytochemicals from Cratoxylum formosum Dyer

Craloxylum formosum Dyer is consumed throughout the year as food and medicine in Thailand. It contains large amounts of chlorogenic acid and quinic acid derivatives. The antioxidative activity of the extract was studied in refined soybean oil coating on rice crackers without any seasoning. They were stored in accelerated oxidation conditions at 40 degrees C, 80% relative humidity (RH) in the dark for 18 days. The oxidative state of each sample was monitored by analyzing of the peroxide value (PV) and thiobarbituric acid reactive substances (TBARS) as well as by odor analysis by quantitative descriptive analysis (QDA). The C formosum extract was more effective than alpha-tocopherol due to metal ions present in the crackers, which resulted in alpha-tocopherol being less effective as an antioxidant. Sensory odor attributes of rice crackers were related more closely to TBARS than to PV values by linear regression analysis. The present study indicated that C. formosum extract was a promising source of a natural food antioxidant and was effective in inhibiting lipid oxidation in rice crackers.

The effect of free Ca2+ on the heat stability and other characteristics of low-heat skim milk powder

Low-heat skim milk powder (SMP), reconstituted to 25% total solids, was found to have poor heat stability. This could be improved by reducing the free Ca2+ concentration to 1.14 mm, or lower, by the addition of either Amberlite IR-120 ion-exchange resin in its sodium form or tri-sodium citrate in skim milk prior to evaporation and spray drying. Reduction in Ca2+ concentration was accompanied by increases in pH, particle size, and kinematic viscosity, and by a reduction in zeta-potential and changes in colour. In-container sterilisation of the reconstituted powder increased particle size, zeta-potential, kinematic viscosity and a* and b* values. However. Ca2+ concentration, pH and whiteness decreased. This study elucidated the importance of Ca2+ concentration and pH on heat stability of low-heat SMP, suggesting that Ca2+ concentration and pH in bulk milk are useful indicators for ensuring that spray dried milk powder has good heat stability. (C) 2009 Elsevier Ltd. All rights reserved.

An efficient shock capturing scheme for the pseudo-unsteady equations representing steady inviscid flow

An efficient algorithm is presented for the solution of the steady Euler equations of gas dynamics. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme is applied to a standard test problem of flow down a channel containing a circular arc bump for three different mesh sizes.

Similarity solutions of the shallow water equations

A one-dimensional shock (bore) reflection problem is discussed for the two-dimensional shallow water equations with cylindrical symmetry. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankine-Hugoniot shock relations.