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A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, which is consistent with the continuous model dynamics. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal decomposition, flow through a cylinder and flow through a sequence of pore throats show the dynamics of the flow with and without surfactant. Finally the numerical method is used to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging. [ABSTRACT FROM AUTHOR]

The racial hierarchy underscoring colonialism persists, organises core-periphery interactions and so undermines International Relations' (IR's) purpose of accounting and explaining to mitigate violence. Despite IR's awareness of its colonialism, it reconstitutes in the hermeneutic's deductive and inductive method via aphasia (calculated forgetting) about its heuristic: diplomacy. The result, analytic-violence or the core's heuristic corrupting interaction with the periphery. Yet, its evasiveness testifies to a meaningfulness beyond IR's hermeneutic. Irretrievably corrupted by its heuristic, IR's hermeneutic is ejected for an altogether new hermeneutic: Producer-Centred Research (PCR). Eschewing deduction and induction, and so colonialism, PCR initiates with abduction or a problem arising from theory and practice to resolve it in terms of rationality because of its, and the problem's, significance. Changing "rationality" to "rationalities" registers the core's rationality as colonialism while preventing it from contaminating PCR's collection and assessment of peripheral practices to determine if they cohere into another rationality. Moreover, treating peripheral practitioners authoritatively, as capable of rationalising themselves and thus equal to rationality, further protects PCR from aphasia. Verifying efficacy shows PCR's decolonisation of the hermeneutic is not entirely replicated externally, amongst IR scholars. The core engages PCR, but it incites violence in the periphery which defends rationality and so is colonialism's bastion, now. [ABSTRACT FROM AUTHOR]

We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of approximate solutions, generated by the scheme corresponding to vanishing diffusive-dispersive scalar conservation laws with a discontinuous coefficient, to the corresponding scalar conservation law with discontinuous coefficient. Finally, the convergence is illustrated by several examples. In particular, it is delineated that the limiting solutions generated by the scheme need not coincide, depending on the relation between diffusion and the dispersion coefficients, with the classical Kružkov−Oleĭnik entropy solutions, but contain nonclassical undercompressive shock waves. [ABSTRACT FROM AUTHOR]

We propose a third-order WENO reconstruction which satisfies the sign property, required for constructing high resolution entropy stable finite difference scheme for conservation laws. The reconstruction technique, which is termed as SP-WENO, is endowed with additional properties making it a more robust option compared to ENO schemes of the same order. The performance of the proposed reconstruction is demonstrated via a series of numerical experiments for linear and nonlinear scalar conservation laws. The scheme is easily extended to multi-dimensional conservation laws. [ABSTRACT FROM AUTHOR]