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Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
Particle-laden flows occur in a wide range of disciplines, from atmospheric flows to renewable energy to turbomachinery. They generally pose a challenging environment for the numerical prediction of particle-induced phenomena due to their…
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
We describe the user interface, governing equations, and numerical methods underpinning the community ocean modeling software called "Oceananigans". Oceananigans development has been lead by the Climate Modeling Alliance to build a…
Integrated sensing and communication (ISAC) is envisioned to be one of the key usage scenarios for the sixth generation (6G) mobile communication networks. While significant progresses have been achieved for the theoretical studies, the…
We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the…
High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the…
The periodic hills simulation case is a well-established benchmark for computational fluid dynamics solvers due to its complex features derived from the separation of a turbulent flow from a curved surface. We study the case with the…
Aside from recent advances in artificial intelligence (AI) models, specialized AI hardware is crucial to address large volumes of unstructured and dynamic data. Hardware-based AI, built on conventional complementary metal-oxidesemiconductor…
Spatial marching methods, in which the flow state is spatially evolved in the downstream direction, can be used to produce low-cost models of flows containing a slowly varying direction, such as mixing layers, jets, and boundary layers. The…
The solution of optimization problems constrained by partial differential equations (PDEs) plays an important role in many areas of science and industry. In this work we present cashocs, a new software package written in Python, which…
The numerical study of physical problems often require integrating the dynamics of a large number of particles evolving according to a given set of equations. Particles are characterized by the information they are carrying such as an…
We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed,…
Developing large-scale foundational datasets is a critical milestone in advancing artificial intelligence (AI)-driven scientific innovation. However, unlike AI-mature fields such as natural language processing, materials science,…
In this work, we detail the GPU-porting of an in-house pseudo-spectral solver tailored towards large-scale simulations of interface-resolved simulation of drop- and bubble-laden turbulent flows. The code relies on direct numerical…