Related papers: A connection between filter stabilization and eddy…
We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…
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…
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…
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents…
We develop a numerical method for simulation of incompressible viscous flows by integrating the technology of random vortex method with the core idea of Large Eddy Simulation (LES). Specifically, we utilize the filtering method in LES,…
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…
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…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…
A new modeling approach for large-eddy simulation (LES) is obtained by combining a `regularization principle' with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
In light of the challenges surrounding convergence and error propagation encountered in Reynolds-averaged Navier-Stokes (RANS) equations with data-driven Reynolds stress closures, researchers commonly attribute these issues to…
Turbulence is a non-local phenomenon and has multiple-scales. Non-locality can be addressed either implicitly or explicitly. Implicitly, by subsequent resolution of all spatio-temporal scales. However, if directly solved for the temporal or…
We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular…
Navier-Stokes equations are well known in modelling of an incompressible Newtonian fluid, such as air or water. This system of equations is very complex due to the non-linearity term that characterizes it. After the linearization and the…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
This paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation [Ida and Taniguchi, Phys. Rev. E 68, 036705 (2003)]. In our previous paper, it was…
This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…
A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes…
We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated…