English
Related papers

Related papers: Versatile Mixed Methods for the Incompressible Nav…

200 papers

In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or…

Numerical Analysis · Mathematics 2026-01-22 Mathias Dauphin , Daniele A. Di Pietro , Jérôme Droniou , Alexandros Skouras

In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…

Analysis of PDEs · Mathematics 2020-05-26 Dieter Bothe , Pierre-Etienne Druet

Inspired by Abbatiello, Feireisl and Novotn\'y, we prove the global existence of dissipative turbulent solution for the compressible Navier-Stokes equations with anisotropic viscous stress tensor on unbounded domain. Our work complements…

Analysis of PDEs · Mathematics 2025-10-24 Ondřej Kreml , Šárka Nečasová , Tong Tang

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…

Computational Physics · Physics 2019-09-04 Nishant Nangia , Boyce E. Griffith , Neelesh A. Patankar , Amneet Pal Singh Bhalla

We study convergence of a mixed finite element-finite volume scheme for the compressible Navier Stokes equations in the isentropic regime under the full range of the adiabatic coefficient gamma for the problem with general non zero…

Numerical Analysis · Mathematics 2020-05-05 Young-Sam Kwon , Antonin Novotny

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier--Stokes equations for which the approximate velocity field is pointwise divergence-free. The method builds on the method presented by Labeur and Wells…

Numerical Analysis · Mathematics 2023-07-04 Sander Rhebergen , Garth N. Wells

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…

Numerical Analysis · Mathematics 2020-05-05 Gabriel N. Gatica , Antonio Márquez , Salim Meddahi

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

Numerical Analysis · Mathematics 2017-07-06 Jean-Claude Latché , Khaled Saleh

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…

Numerical Analysis · Mathematics 2015-05-20 David Shirokoff , Rodolfo Ruben Rosales

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in…

Numerical Analysis · Mathematics 2017-12-06 P. L. Lederer , C. Merdon , J. Schöberl

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…

Numerical Analysis · Mathematics 2022-11-28 Hailong Qiu

For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in…

Numerical Analysis · Mathematics 2024-10-16 Nicolás Espinoza-Contreras , Gabriel Barrenechea , Ernesto Castillo , Douglas Pacheco

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete…

Numerical Analysis · Mathematics 2026-05-05 Takeharu Matsuda , Satoshi Ii

We present a numerical method for two-phase incompressible Navier-Stokes equation with jump discontinuity in the normal component of the stress tensor and in the material properties. Although the proposed method is only first-order…

Computational Physics · Physics 2021-08-25 Hyuntae Cho , Myungjooo Kang

We develop and analyse an adaptive fully mixed finite element method for stationary generalized bioconvective flows, where the Navier--Stokes equations with concentration-dependent viscosity are coupled with a conservation law for swimming…

Numerical Analysis · Mathematics 2026-01-14 Eligio Colmenares , Ricardo Ruiz-Baier , Dalidet Sanhueza

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to full discrete conservation of…

Numerical Analysis · Mathematics 2024-09-04 Lukas Lundgren , Murtazo Nazarov

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