A numerical investigation on the heat flow in the process of oil-water displacement in SDPSO

Spar Drilling Production Storage and Offloading (SDPSO) is a new type of deep ocean platform developed in recent years. The process of oil-water displacement is used for oil storage and offloading and the research on the accompanying heat flow has been significant. The wax precipitation and solidification at low temperature will particularly affect the flowing of oil in the displacement process. When the heat flow is concerned, numerical simulation requires large computation. It is necessary to develop an efficient numerical method for this calculation. As a kind of interface tracking method, the volume of fluid (VOF) method needs less computing resources compared with other multiphase numerical methods. As for thermal expressions, there are mainly two kinds of governing equations, i.e. temperature equation and enthalpy equation, and two kinds of interpolation scheme of heat conductivity, i.e. algebraic interpolation scheme and harmonic interpolation scheme. There is a need to find out which combination of governing equation and interpolation scheme of heat conductivity would result in a better precision for the heat flow. Therefore, four non-isothermal solvers, corresponding to the four combinations, are established. After comparison with an analytical solution, it is found that the temperature equation together with the harmonic interpolation scheme of heat conductivity results in better precision.

Visualizing fuzzy sets using opacity-varying freeform diagrams

As an extension of classical sets, fuzzy sets allow their containing elements to have continuous membership, which broadens its applications in various domains. In order to visualize the uncertain owner–member relationship, we design an intuitive diagram to visualize fuzzy sets. The diagram has a freeform boundary, which allows a clear layout of the data. In addition, the opacity of the diagram reveals the uncertainty of the membership. Physical simulation and bi-harmonic interpolation are introduced to generate the proposed diagram. We test our method with different fuzzy sets. The results show that our method is efficient to generate intuitive visualization of fuzzy sets.

Harmonic interpolation based on Radon projections along the sides of regular polygons

Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.