Related papers: Mesh-Free Hydrodynamic Stability
We develop a one-dimensional model for the unsteady fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. A beam equation, which accounts for both transverse bending rigidity and nonlinear…
We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Full details about the scheme…
Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…
The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us…
Motivated by the experimental ability to produce monodisperse particles in microfluidic devices, we study theoretically the hydrodynamic stability of driven and active crystals. We first recall the theoretical tools allowing to quantify the…
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…
The possibility that the magnetic shear-flow instability (MRI, Balbus-Hawley instability) might give rise to turbulence in a cylindric Couette flow is investigated through numerical simulations. The study is linear and the fluid flow is…
The resolvent formulation of the Navier$\text{--}$Stokes equations gives a means for the characterization and prediction of features of turbulent flows$\text{---}$such as statistics, structures and their nonlinear…
Using a new numerical code we have carried out two-dimensional simulations of the nonlinear evolution of unstable sheared magnetohydrodynamic flows. We considered two cases: a strong magnetic field (Alfven Mach number, M_a = 2.5) and a weak…
The interaction of a Mach 1.45 shock wave with a perturbed planar interface between sulphur hexafluoride and air is studied through high-resolution two-dimensional (2D) and three-dimensional (3D) shock-capturing adaptive mesh refinement…
Effective stormwater treatment infrastructures are crucial for mitigating the adverse effects of runoff on urban water quality. However, designing cost-effective treatment systems can be challenging due to complex turbulent flow dynamics.…
We analyse numerically the linear stability of a liquid metal flow in a rectangular duct with perfectly electrically conducting walls subject to a uniform transverse magnetic field. A non-standard three dimensional vector stream…
To effectively handle flows characterized by strong backflow and multiple open boundaries within particle-based frameworks, this study introduces three enhancements to improve the consistency, independence, and accuracy of the buffer-based…
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear…
We develop a gradient based optimization approach for the equations of compressible, Lagrangian hydrodynamics and demonstrate how it can be employed to automatically uncover strategies to control hydrodynamic instabilities arising from…
Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because…
Stationary and instationary Stokes and Navier-Stokes flows are considered on two-dimensional manifolds, i.e., on curved surfaces in three dimensions. The higher-order surface FEM is used for the approximation of the geometry, velocities,…
Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…