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We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data…

Analysis of PDEs · Mathematics 2021-06-07 Elisabeth Diehl , Johannes Haubner , Michael Ulbrich , Stefan Ulbrich

We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…

Numerical Analysis · Mathematics 2026-05-19 Aparna Bansal , Nicolas A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…

Numerical Analysis · Mathematics 2010-11-01 Thierry Gallouët , Laura Gastaldo , Jean-Claude Latché , Raphaele Herbin

In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached…

Numerical Analysis · Mathematics 2022-01-10 Yabin Zhang , Adrianna Gillman , Shravan Veerapaneni

We introduce new control-volume finite-element discretization schemes suitable for solving the Stokes problem. Within a common framework, we present different approaches for constructing such schemes. The first and most established strategy…

Numerical Analysis · Mathematics 2025-02-05 Martin Schneider , Timo Koch

We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…

Numerical Analysis · Mathematics 2026-05-07 Aziz Takhirov , Driss Yakoubi

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different…

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier-Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained…

Computational Physics · Physics 2015-08-13 Alexandros Syrakos , Apostolos Goulas

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…

Numerical Analysis · Mathematics 2022-02-02 Jean-Luc Guermond , Martin Kronbichler , Matthias Maier , Bojan Popov , Ignacio Tomas

In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…

Numerical Analysis · Mathematics 2026-01-09 Harald Garcke , Robert Nürnberg

We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…

Numerical Analysis · Mathematics 2023-06-27 Veronica Anaya , Ruben Caraballo , Ricardo Ruiz-Baier , Hector Torres

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…

Fluid Dynamics · Physics 2025-08-22 Xinjie Ji , Changxiao Nigel Shen , Wim M. van Rees

Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…

Numerical Analysis · Mathematics 2020-07-14 Hendrik Ranocha , Lisandro Dalcin , Matteo Parsani

This paper provides mathematical analysis of an elementary fully discrete finite difference method applied to inhomogeneous (non-constant density and viscosity) incompressible Navier-Stokes system on a bounded domain. The proposed method…

Numerical Analysis · Mathematics 2023-02-28 Kohei Soga

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

In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global…

Numerical Analysis · Mathematics 2022-10-28 Danica Basaric , Maria Lukacova-Medvidova , Hana Mizerova , Bangwei She , Yuhuan Yuan

We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…

Numerical Analysis · Mathematics 2025-03-11 Hanne Hardering , Simon Praetorius

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Numerical Analysis · Mathematics 2019-02-01 Victor DeCaria , William Layton , Haiyun Zhao

In this paper we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier-Stokes equations. The algorithm uses a finite volume approach that…

Fluid Dynamics · Physics 2019-02-15 Matthew Emmett , Emmanuel Motheau , Weiqun Zhang , Michael Minion , John B. Bell