Related papers: A Convex Approach to Hydrodynamic Analysis
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
We consider the motion of incompressible viscous fluid in a rectangle, imposing the periodicity condition in one direction and the no-slip boundary condition in the other. Assuming that the flow is subject to an external random force, white…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
This paper numerically investigates the instability characteristics of decelerating flows. The flow dynamics and temporal evolution of coherent structures in a diverging section with mild spatial pressure gradient are analyzed using…
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
The identification of stream in the straight pipe as a flexible rod has allowed to present the criterion expression for determination of transition of the laminar flow regime to the turbulent as a loss of stability of the rectilinear static…
We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega…
For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal…
The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have…
The stability of a three-dimensional, incompressible, viscous flow through a finite-length duct is studied. A divergence-free basis technique is used to formulate the weak form of the problem. A SUPG (streamingline upwind Petrov-Galerkin)…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
This study extends the flow measurement method initially proposed in [22] to three-dimensional scenarios, addressing the growing need for accurate and efficient non-contact flow measurement techniques in complex hydrodynamic environments.…
Modal instabilities in a flow through a channel at high Reynolds and Mach numbers are studied for three-dimensional perturbations. In addition to the Tollmien-Schlichting modes, there exist higher modes in a channel flow that do not have a…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…
This paper carries out a linear stability analysis of a plane Couette flow in a porous layer underlying a fluid layer where the porous layer is anisotropic and inhomogeneous. The plane Couette flow is induced due to the uniform movement of…
The transition between kinetic and hydrodynamic regimes of the one-dimensional two-stream instability is numerically analyzed, and the correction coefficients to the well-known textbook formulae are calculated. The approximate expressions…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use…