English
Related papers

Related papers: New SAV-pressure correction methods for the Navier…

200 papers

The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are…

Numerical Analysis · Mathematics 2025-01-14 Melvin Creff , Jean-Luc Guermond

Classical Navier-Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier-Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the re-casted…

Fluid Dynamics · Physics 2021-09-16 M. H. Lakshminarayana Reddy , S. Kokou Dadzie

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

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

In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the…

Numerical Analysis · Mathematics 2026-04-16 Bikram Bir , Deepjyoti Goswami , Amiya K. Pani

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the…

Chaotic Dynamics · Physics 2009-11-10 L. Ts. Adzhemyan , N. V. Antonov , J. Honkonen , T. L. Kim

We present a second-order monolithic method for solving incompressible Navier--Stokes equations on irregular domains with quadtree grids. A semi-collocated grid layout is adopted, where velocity variables are located at cell vertices, and…

Numerical Analysis · Mathematics 2022-06-01 Hyuntae Cho , Yesom Park , Myungjoo Kang

In this paper, we present a novel strategy to systematically construct linearly implicit energy-preserving schemes with arbitrary order of accuracy for Hamiltonian PDEs. Such novel strategy is based on the newly developed exponential scalar…

Numerical Analysis · Mathematics 2023-07-27 Yonghui Bo , Yushun Wang , Wenjun Cai

In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…

In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…

Numerical Analysis · Mathematics 2025-12-03 Charles M. Elliott , Achilleas Mavrakis

We propose first- and second-order time discretization schemes for the coupled Cahn--Hilliard--Navier--Stokes model, leveraging the incremental viscosity splitting (IVS) method. The schemes combine the scalar auxiliary variable method and…

Numerical Analysis · Mathematics 2025-08-05 Baolin Kuang , Hongfei Fu , Xiaoli Li

In this paper, the strong formulation of the generalised Navier-Stokes momentum equation is investigated. Specifically, the formulation of shear-stress divergence is investigated, due to its effect on the performance and accuracy of…

Fluid Dynamics · Physics 2023-10-11 Josip Basic , Martina Basic , Branko Blagojevic

A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…

General Mathematics · Mathematics 2023-06-28 R. K. Michael Thambynayagam

A mixed finite element method for the Navier-Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier-Stokes equations and the classical theory…

Numerical Analysis · Mathematics 2016-03-31 Jason S. Howell , Noel J. Walkington

In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an…

Numerical Analysis · Mathematics 2021-08-26 Shuvam Sen , Tony W. H. Sheu

We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary…

Analysis of PDEs · Mathematics 2017-08-09 Maxim A. Olshanskii , Leo G. Rebholz , Abner J. Salgado

We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or…

Numerical Analysis · Mathematics 2021-08-03 Santolo Leveque , John W. Pearson

This paper extends a new class of positivity-preserving, entropy stable spectral collocation schemes developed for the one-dimensional compressible Navier-Stokes equations in [1,2] to three spatial dimensions. The new high-order schemes are…

Numerical Analysis · Mathematics 2021-11-18 Nail K. Yamaleev , Johnathon Upperman

We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…

Analysis of PDEs · Mathematics 2018-02-13 Michele Coti Zelati , Nathan Glatt-Holtz , Konstantina Trivisa

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

Analysis of PDEs · Mathematics 2016-07-15 Šimon Axmann , Piotr B. Mucha , Milan Pokorný