In this paper, stable and “low-diffusive” multidimensional interface capturing (IC) schemes using slope limiters are discussed. It is known that direction-by-direction slope-limited MUSCL schemes create geometrical artefacts and thus return a poor accuracy. We here focus on this particular issue and show that the reconstruction of gradient directions are an important factor of accuracy. The use...

A novel finite-volume interface (contact) capturing method is presented for simulation of multi-component compressible flows with high density ratios and strong shocks. In addition, the materials on the two sides of interfaces can have significantly different equations of state. Material boundaries are identified through an interface function, which is solved in concert with the governing equat...

We provide an overview of some of the interface-tracking and interface-capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces. This category of flow problems includes fluid–particle, fluid–object and fluid–structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. Both classes of techniq...

In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating $d$-dimensional piecewise continuous functions and solving elliptic interface problems is developed. There are three novel features in the present network; namely, (i) jump discontinuities accurately captured, (ii) it completely shallow, comprising only one hidden layer, (iii) mesh-free partial differe...