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We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into…

Fluid Dynamics · Physics 2025-05-21 Alexandros Kontogiannis , Richard Hodgkinson , Emily L. Manchester

In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is…

Analysis of PDEs · Mathematics 2024-04-30 Seongyeon Kim , Sunghwan Moon , Ihyeok Seo

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…

Numerical Analysis · Mathematics 2020-11-20 Tiffany Fan , Kailai Xu , Jay Pathak , Eric Darve

For the 2D incompressible Navier-Stokes equations, with given hypothetical non smooth data at time $T > 0 $that may not correspond to an actual solution at time $T$, a previously developed stabilized backward marching explicit leapfrog…

Numerical Analysis · Mathematics 2024-11-25 Alfred S. Carasso

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…

Fluid Dynamics · Physics 2022-07-13 James Gabbard , Thomas Gillis , Philippe Chatelain , Wim M. van Rees

We consider a non-linear Bayesian data assimilation model for the periodic two-dimensional Navier-Stokes equations with initial condition modelled by a Gaussian process prior. We show that if the system is updated with sufficiently many…

Statistics Theory · Mathematics 2024-07-10 Richard Nickl , Edriss S. Titi

We consider the inverse problem of determining a compact Riemannian manifold with boundary from fixed time observations of the solution, restricted to a small subset in space, for the Navier-Stokes system with a local source on the…

Analysis of PDEs · Mathematics 2026-02-10 Yavar Kian , Lauri Oksanen , Ziyao Zhao

An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform…

Analysis of PDEs · Mathematics 2025-08-05 Yuxi Hu , Yachun Li

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…

Numerical Analysis · Mathematics 2023-01-16 Erik Burman , Deepika Garg , Janosch Preuss

We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider the two boundary problems: impermeable wall and inflow…

Analysis of PDEs · Mathematics 2025-01-08 Xushan Huang , Moon-Jin Kang , Jeongho Kim , Hobin Lee

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…

Numerical Analysis · Mathematics 2017-07-12 Sébastien Court , Michel Fournié

Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a cylindrical domain of height $\varepsilon $ with…

Analysis of PDEs · Mathematics 2021-03-29 Ken Furukawa , Yoshikazu Giga , Matthias Hieber , Amru Hussein , Takahito Kashiwabara , Marc Wrona

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient…

Numerical Analysis · Mathematics 2015-08-27 Eduard Feireisl , Radim Hošek , David Maltese , Antonín Novotný

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…

Numerical Analysis · Mathematics 2023-05-03 Veit Krause , Axel Voigt

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

Inverse problems in computational mechanics consist of inferring physical fields that are latent in the model describing some observable fields. For instance, an inverse problem of interest is inferring the Reynolds stress field in the…

Computational Physics · Physics 2020-06-24 Carlos A. Michelén Ströfer , Xinlei Zhang , Heng Xiao , Olivier Coutier-Delgosha

In this paper we give a new formulation of the compressible Navier-Stokes by introducing an suitable effective velocity $v=u+\n\va(\rho)$ provided that the viscosity coefficients verify the algebraic relation of \cite{BD}. We give in…

Analysis of PDEs · Mathematics 2014-11-21 Boris Haspot

Recently, for periodic initial data with initial density allowed to vanish, Huang and Li [1] establish the global existence of strong and weak solutions for the two-dimensional compressible Navier{Stokes equations with no restrictions on…

Analysis of PDEs · Mathematics 2012-06-21 Fei Jiang

We study the three-dimensional Navier--Stokes equations of rotating incompressible viscous fluids with periodic boundary conditions. The asymptotic expansions, as time goes to infinity, are derived in all Gevrey spaces for any Leray-Hopf…

Analysis of PDEs · Mathematics 2020-07-02 Luan T. Hoang , Edriss S. Titi

We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…

Fluid Dynamics · Physics 2016-08-31 Davide Modesti , Sergio Pirozzoli