English
Related papers

Related papers: Operator splitting for two-dimensional incompressi…

200 papers

Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work…

Fluid Dynamics · Physics 2024-11-12 Agustina Felipe , Ruben Sevilla , Oubay Hassan

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is…

Analysis of PDEs · Mathematics 2024-02-26 Vincent R. Martinez

We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , L. Ridgway Scott

We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…

Fluid Dynamics · Physics 2026-04-16 Ramansh Sharma , Matthew Lowery , Houman Owhadi , Varun Shankar

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

Optimization and Control · Mathematics 2013-07-22 Cameron Talischi , Glaucio H. Paulino

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order…

Numerical Analysis · Mathematics 2017-11-27 Marian Piatkowski , Steffen Müthing , Peter Bastian

We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid to approximate the nonlinear…

Numerical Analysis · Mathematics 2016-12-23 Javier de Frutos , Bosco García-Archilla , Julia Novo

We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.

Analysis of PDEs · Mathematics 2015-11-10 Tarek Elgindi , Wenqing Hu , Vladimir Sverak

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…

Numerical Analysis · Mathematics 2022-12-20 Shi Jin , Yiwen Lin

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…

Analysis of PDEs · Mathematics 2020-07-28 Zhilei Liang , Dehua Wang

We construct solutions to the Navier-Stokes equations on $\mathbf{R}^2$ with an arbitrary number of stagnation points which merge and split along trajectories that can be prescribed freely, up to a small deformation.

Analysis of PDEs · Mathematics 2025-10-02 Isidro Benaroya , Alberto Enciso , Daniel Peralta-Salas

High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…

Numerical Analysis · Mathematics 2025-12-22 Kelong Cheng , Jingwei Sun , Hong Zhang

This paper deals with a time-split explicit/implicit approach for solving a two-dimensional hydrodynamic flow model with appropriate initial and boundary conditions. The time-split technique is employed to upwind the convection term and to…

Numerical Analysis · Mathematics 2024-12-18 Eric Ngondiep

Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…

Numerical Analysis · Mathematics 2023-08-14 Raymond J. Spiteri , Arash Tavassoli , Siqi Wei , Andrei Smolyakov

In this paper, we prove that a local weak solution to the $d$-dimensional incompressible Navier-Stokes equations ($d \geq 2$) can be constructed by taking the hydrodynamic limit of a velocity-discretized Boltzmann equation with a simplified…

Analysis of PDEs · Mathematics 2026-04-15 Zhongyang Gu , Xin Hu , Pritpal Matharu , Bartosz Protas , Makiko Sasada , Tsuyoshi Yoneda

Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…

Numerical Analysis · Mathematics 2019-04-12 Philipp W. Schroeder , Christoph Lehrenfeld , Alexander Linke , Gert Lube

We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…

Numerical Analysis · Mathematics 2025-04-22 Cappanera Loic , Giordano Salvatore

We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for…

Computational Physics · Physics 2022-06-03 Sergey A. Dyachenko , Anatoly Zlotnik , Alexander O. Korotkevich , Michael Chertkov

We consider a model for flow of liquid and gas in a pipe. We assume that the gas is ideal and that the liquid is incompressible. Under this assumption the resulting equations, expressing conservation of mass and momentum, splits into two…

Numerical Analysis · Mathematics 2019-10-15 Nils Henrik Risebro , Adrian Montgomery Ruf

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…

Numerical Analysis · Mathematics 2018-02-14 Sebastian Reuther , Axel Voigt