Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Effect of seasonal variation on some physical properties and heat stability of milk subjected to ultra-high temperature and in-container sterilisation

Heat stability was evaluated in bulk raw milk, collected throughout the year and subjected to ultra-high temperature (UHT) or in-container sterilisation, with and without added calcium chloride (2 mM), disodium hydrogen phosphate (DSHP, 10 mM) and trisodium citrate (TSC, 10 mM). More sediment was observed following in-container sterilisation (0.24%) compared with UHT (0.19%). Adding CaCl2 made the milk more unstable to UHT than to in-container sterilisation, while adding DSHP and TSC made the milk more unstable during in-container sterilisation than to UHT processing, although TSC addition increased the sediment formed by UHT processing. Better heat stability was observed in autumn and winter than in spring and summer following UHT. However, following in-container sterilisation, samples with added stabilising salts showed significantly improved heat stability in autumn, whereas with added CaCl2, the best heat stability was observed in spring. No correlation was found between urea and heat stability. DSHP and TSC made the milk more unstable during in-container sterilisation than to UHT processing, although TSC addition increased the sediment formed by UHT processing. Better heat stability was observed in autumn and winter than in spring and summer following UHT. However, following in-container sterilisation, samples with added stabilising salts showed significantly improved heat stability in autumn, whereas with added CaCl2, the best heat stability was observed in spring. No correlation was found between urea and heat stability.