Irina Shishkina | Searcharxiv

arXiv2026

Comparative study of different quadrature methods for cut elements

The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some available as open-source implementations. This work reviews these open-sources codes and the methods used. Furthermore, benchmarking examples are developed for 2D and 3D geometries. Implicit and explicit boundary descriptions are available for all models. The different examples test the efficiency, accuracy, versatility, and robustness of the codes. Special focus is set on the influence of the input parameter, which controls the desired quadrature order, on the actual integration error. A detailed comparison of the discussed codes is carried out. The benchmarking allows a conclusive comparison and presents a valuable tool for future code development. All tests are published in an accompanying open-source repository.

cs.CE↗

arXiv2025

Wetting simulation of the porous structure of a heat pipe using an eXtended Discontinuous Galerkin Method and a Parameterized Level-Set

We perform high-order simulations of two-phase flows in capillaries, with and without evaporation. Since a sharp-interface model is used, singularities can arise at the three-phase contact line, where the fluid-fluid interface interacts with the capillary wall. These singularities are especially challenging when a highly accurate, high-order method with very little numerical diffusion is used for the flow solver. In this work, we employ the eXtended Discontinuous Galerkin (XDG) method, which has a very high accuracy but a severe limit regarding e.g., the time-step restriction. To address this challenge and enhance the stability of our numerical method we introduce a novel approach for representing a moving interface in the case of two-phase flows. We propose a global analytical representation of the interface-describing level-set field, defined by a small set of time-dependent parameters. Noteworthy for its simplicity and efficiency, this method effectively addresses the inherent complexity of two-phase flow problems. Furthermore, it significantly improves numerical stability and enables the use of larger time steps, ensuring both reliability and computational efficiency in our simulations. We compare different analytic expressions for level-set representation, including the elliptic function and the fourth-order polynomial, and validate the method against established literature data for capillary rise, both with and without evaporation. These results highlight the effectiveness of our approach in resolving complex interfacial dynamics.

physics.flu-dyn↗