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In this paper, we investigate the use of compactly supported divergence-free wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in…

Numerical Analysis · Mathematics 2025-10-20 Erwan Deriaz , Valérie Perrier

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test…

Analysis of PDEs · Mathematics 2015-06-03 Eduard Feireisl , Bum Ja Jin , Antonin Novotny

We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…

Numerical Analysis · Mathematics 2025-10-02 Boris D. Andrews , Patrick E. Farrell

The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic…

Analysis of PDEs · Mathematics 2016-01-08 Miroslav Bulíček , Piotr Gwiazda , Endre Süli , Agnieszka Świerczewska-Gwiazda

A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus…

Fluid Dynamics · Physics 2021-02-24 Pankaj Jagad , Abdullah Abukhwejah , Mamdouh Mohamed , Ravi Samtaney

In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of…

Numerical Analysis · Mathematics 2024-08-21 Gabriel R. Barrenechea , Ernesto Castillo , Douglas R. Q. Pacheco

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…

Analysis of PDEs · Mathematics 2020-12-24 Marco Cannone , Grzegorz Karch , Dominika Pilarczyk , Gang Wu

In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…

Numerical Analysis · Mathematics 2016-06-29 Christoph Lehrenfeld , Joachim Schöberl

In this paper we consider the flow of two incompressible, viscous and immiscible fluids in a bounded domain, with different densities and viscosities. This model consists of a coupled system of Navier-Stokes and Mullins-Sekerka type parts,…

Analysis of PDEs · Mathematics 2025-05-13 Helmut Abels , Andrea Poiatti

We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the…

Numerical Analysis · Mathematics 2024-08-20 Haijun Gao , Xi Li , Minfu Feng

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…

Numerical Analysis · Mathematics 2021-03-17 Walter Boscheri , Lorenzo Pareschi

We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with…

Numerical Analysis · Mathematics 2023-02-28 Dominic Breit , Alan Dodgson

We consider global in time solutions of the Navier-Stokes-Fourier system describing the motion of a general compressible, viscous and heat conducting fluid far from equilibirum. Using a new concept of weak solution suitable to accommodate…

Analysis of PDEs · Mathematics 2021-09-03 Eduard Feireisl , Young-Sam Kwon

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

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 consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…

Analysis of PDEs · Mathematics 2015-11-17 Ondrej Kreml , Vaclav Macha , Sarka Necasova , Aneta Wroblewska-Kaminska

The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…

Numerical Analysis · Mathematics 2024-08-26 Michael Neilan , Maxim Olshanskii

We study conservation properties of Galerkin methods for the incompressible Navier-Stokes equations, without the divergence constraint strongly enforced. In typical discretizations such as the mixed finite element method, the conservation…

Numerical Analysis · Mathematics 2017-04-05 Sergey Charnyi , Timo Heister , Maxim A. Olshanskii , Leo G. Rebholz

We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered…

Analysis of PDEs · Mathematics 2015-09-28 P. Kalita , G. Łukaszewicz