Development of accurate, robust liquid equations of state for multi-phase CFD simulations with a modified AUSM+-up scheme

Eight equations of state (EOS) have been evaluated for the simulation of compressible liquid water properties, based on empirical correlations, the principle of corresponding states and thermodynamic relations. The IAPWS-IF97 EOS for water was employed as the reference case. These EOSs were coupled to a modified AUSM+-up convective flux solver to determine flow profiles for three test cases of differing flow conditions. The impact of the non-viscous interaction term discretisation scheme, interfacial pressure method and selection of low-Mach number diffusion were also compared. It was shown that a consistent discretisation scheme using the AUSM+-up solver for both the convective flux and the non-viscous interfacial term demonstrated both robustness and accuracy whilst facilitating a computationally cheaper solution than discretisation of the interfacial term independently by a central scheme. The simple empirical correlations gave excellent results in comparison to the reference IAPWS-IF97 EOS and were recommended for developmental work involving water as a cheaper and more accurate EOS than the more commonly used stiffened-gas model. The correlations based on the principles of corresponding-states and the modified Peng-Robinson cubic EOS also demonstrated a high degree of accuracy, which is promising for future work with generic fluids. Further work will encompass extension of the solver to multiple dimensions and to account for other source terms such as surface tension, along with the incorporation of phase changes. © 2013.

Simulations of thermal upgrading methods for oil shale reservoirs

This paper analyzes reaction and thermal front development in porous reservoirs with reacting flows, such as those encountered in shale oil extraction. A set of dimensionless parameters and a 3D code are developed in order to investigate the important physical and chemical variables of such reservoirs when heated by in situ methods. This contribution builds on a 1D model developed for the precursor study to this work. Theory necessary for this study is presented, namely shale decomposition chemical mechanisms, governing equations for multiphase flow in porous media and necessary closure models. Plotting the ratio of the thermal wave speed to the fluid speed allows one to infer that the reaction wave front ends where this ratio is at a minimum. The reaction front follows the thermal front closely, thus allowing assumptions to be made about the extent of decomposition solely by looking at thermal wave progression. Furthermore, this sensitivity analysis showed that a certain minimum permeability is required in order to ensure the formation of a traveling thermal wave. It was found that by studying the non-dimensional governing parameters of the system one can ascribe characteristic values for these parameters for given initial and boundary conditions. This allows one to roughly predict the performance of a particular method on a particular reservoir given approximate values for initial and boundary conditions. Channelling and flow blockage due to carbon residue buildup impeded each method's performance. Blockage was found to be a result of imbalanced heating. Copyright 2012, Society of Petroleum Engineers.

Multi scale shape index for 3D object recognition

We present Multi Scale Shape Index (MSSI), a novel feature for 3D object recognition. Inspired by the scale space filtering theory and Shape Index measure proposed by Koenderink & Van Doorn [6], this feature associates different forms of shape, such as umbilics, saddle regions, parabolic regions to a real valued index. This association is useful for representing an object based on its constituent shape forms. We derive closed form scale space equations which computes a characteristic scale at each 3D point in a point cloud without an explicit mesh structure. This characteristic scale is then used to estimate the Shape Index. We quantitatively evaluate the robustness and repeatability of the MSSI feature for varying object scales and changing point cloud density. We also quantify the performance of MSSI for object category recognition on a publicly available dataset. © 2013 Springer-Verlag.

Cabaret finite-difference schemes for the one-dimensional Euler equations

In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one-dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two-time-layer form, which makes it most simple and robust. Supersonic and subsonic shock-tube tests are used to compare the new schemes with several well-known second-order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second-order Roe scheme with MUSCL flux splitting.

Numerical modelling of chirality-Induced bi-Directional swimming of artificial flagella

Biomimetic micro-swimmers can be used for various medical applications, such as targeted drug delivery and micro-object (e.g. biological cells) manipulation, in lab-on-a-chip devices. Bacteria swim using a bundle of flagella (flexible hair-like structures) that form a rotating cork-screw of chiral shape. To mimic bacterial swimming, we employ a computational approach to design a bacterial (chirality-induced) swimmer whose chiral shape and rotational velocity can be controlled by an external magnetic field. In our model, we numerically solve the coupled governing equations that describe the system dynamics (i.e. solid mechanics, fluid dynamics and magnetostatics). We explore the swimming response as a function of the characteristic dimensionless parameters and put special emphasis on controlling the swimming direction. Our results provide fundamental physical insight on the chirality-induced propulsion, and it provides guidelines for the design of magnetic bi-directional micro-swimmers. © 2013 The Author(s) Published by the Royal Society. All rights reserved.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.