Related papers: Unstructured un-split geometrical Volume-of-Fluid …
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Unsigned Distance Fields (UDFs) provide a flexible representation for 3D shapes with arbitrary topology, including open and closed surfaces, orientable and non-orientable geometries, and non-manifold structures. While recent neural…
The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…
Existing UV mapping algorithms are designed to operate on well-behaved meshes, instead of the geometry representations produced by state-of-the-art 3D reconstruction and generation techniques. As such, applying these methods to the volume…
This work combines the consistency in lower-order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured non-uniform meshes. This…
Volume of fluid (VOF) methods are extensively used to track fluid interfaces in numerical simulations, and many VOF algorithms require that the interface be reconstructed geometrically. For this purpose, the Piecewise Linear Interface…
This paper presents a three-dimensional framework for simulating dynamic wetting phenomena using the volume of fluid (VOF) method, implemented in Basilisk. A geometric interpolation scheme is developed to obtain an accurate and reliable…
For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
In this work, we propose an automatic mesh generation algorithm, FlowMesher, which can be used to generate unstructured meshes for mesh domains in any shape with minimum (or even no) user intervention. The approach can generate high-quality…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
Recent generative models can create visually plausible 3D representations of objects. However, the generation process often allows for implicit control signals, such as contextual descriptions, and rarely supports bold geometric distortions…
Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore,…
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…
Incremental scene reconstruction is essential to the navigation in robotics. Most of the conventional methods typically make use of either TSDF (truncated signed distance functions) volume or neural networks to implicitly represent the…