title: Completeness, conservation and error in SPH for fluids

authors: Vaughan, G.L.

subjects: mathematics

abstract: Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low-order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright ©2007 John Wiley & Sons, Ltd.

text: Completeness, conservation and error in SPH for fluids Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low-order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright ©2007 John Wiley & Sons, Ltd.

year: 2008

title: The policy of direct provision in Ireland: A violation of asylum seeker’s right to an adequate standard of housing

authors: Breen, Claire

subjects: Ireland

abstract: This article considers Ireland's policy of Direct Provision, which curtails severely the social welfare entitlements of asylum seekers. This article sets out the rights of asylum seekers in Ireland and explains the policy of Direct Provision. It analyses the right to adequate housing as provided for within the United Nations and the European legal frameworks. It acknowledges that such rights are subject to some limitations but argues that Ireland's policy of Direct Provision violates asylum seekers’ rights to an adequate standard of living, with particular focus on the right to adequate housing and the interrelated rights to food and health. It further argues that such limitations are discriminatory and that they undermine the fundamental principles of equality and human dignity. The article concludes that a correct interpretation of international and domestic law suggests that Ireland must abolish the policy of Direct Provision and revert to according social welfare entitlements on the basis of need rather than nationality.

text: The policy of direct provision in Ireland: A violation of asylum seeker’s right to an adequate standard of housing This article considers Ireland's policy of Direct Provision, which curtails severely the social welfare entitlements of asylum seekers. This article sets out the rights of asylum seekers in Ireland and explains the policy of Direct Provision. It analyses the right to adequate housing as provided for within the United Nations and the European legal frameworks. It acknowledges that such rights are subject to some limitations but argues that Ireland's policy of Direct Provision violates asylum seekers’ rights to an adequate standard of living, with particular focus on the right to adequate housing and the interrelated rights to food and health. It further argues that such limitations are discriminatory and that they undermine the fundamental principles of equality and human dignity. The article concludes that a correct interpretation of international and domestic law suggests that Ireland must abolish the policy of Direct Provision and revert to according social welfare entitlements on the basis of need rather than nationality.

year: 2008

title: Katoa: A descriptive, comparative and historical analysis

authors: Wessels, Kanauhea Janion

subjects: discontinuous quantification

abstract: Katoa, approximately translated as ‘all, every’, functions as the universal quantifier in te reo Māori (the Māori language), inherited from Proto Polynesian *katoa. Less well known is its occurrence as a postnominal modifier in singular noun phrases, contributing the meaning of ‘whole’, and as a nominal head meaning ‘all (of them), the whole (of it)’. As a postverbal modifier, katoa can quantify a subject noun phrase with the same meanings of ‘all, every’ and ‘whole’, and it can modify situations expressed by the verb, meaning ‘wholly, completely’. In this paper, we examine the behaviour of katoa in te reo Māori, comparing some properties of katoa with the behaviour of quantifiers in related Polynesian languages. This, in turn, informs our understanding of the prehistory of quantification in Polynesian, where we observe evidence of both retention and replacement of quantifier forms.

text: Katoa: A descriptive, comparative and historical analysis Katoa, approximately translated as ‘all, every’, functions as the universal quantifier in te reo Māori (the Māori language), inherited from Proto Polynesian *katoa. Less well known is its occurrence as a postnominal modifier in singular noun phrases, contributing the meaning of ‘whole’, and as a nominal head meaning ‘all (of them), the whole (of it)’. As a postverbal modifier, katoa can quantify a subject noun phrase with the same meanings of ‘all, every’ and ‘whole’, and it can modify situations expressed by the verb, meaning ‘wholly, completely’. In this paper, we examine the behaviour of katoa in te reo Māori, comparing some properties of katoa with the behaviour of quantifiers in related Polynesian languages. This, in turn, informs our understanding of the prehistory of quantification in Polynesian, where we observe evidence of both retention and replacement of quantifier forms.

year: 2024