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In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
A spectral method using associated Legendre functions with algebraic mapping is developed for a linear stability analysis of wake vortices. These functions serve as Galerkin basis functions, capturing correct analyticity and boundary…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
The nonlinear development of finite amplitude disturbances in mixed convection flow in a heated vertical annulus is studied by direct numerical simulation. The unsteady Navier Stokes equations are solved numerically by a spectral method for…
Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition…
This article proposes a new statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired from some Monte-Carlo algorithms used in linear transport physics, where virtual particles are…
Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex,…
This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on…
The Lattice-Boltzmann method is a mesoscopic approach for solving hydrodynamic problems involving both laminar and turbulent fluids. Although the suitability for the former cases is supported by a myriad of studies, turbulent flows always…
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
For a prescribed deterministic kinetic energy we use convex integration to construct analytically weak and probabilistically strong solutions to the 3D incompressible Navier-Stokes equations driven by a linear multiplicative stochastic…
We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conducting ideal polytropic gas in the one-dimensional half-space. A rarefaction wave and its superposition with a…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution…
A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a…
We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems,…
A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution…
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…