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We study the sedimentation of finite-size inertial particles in a Rayleigh-Taylor-like setup using state-of-the-art direct numerical simulations. The falling particles are observed to produce two distinct regions: a leading mixing layer…
A popular version of the finite strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of Mooney-Rivlin type; it…
The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered…
We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each…
Rayleigh-B\'enard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
An approach that extends equilibrium thermodynamics principles to out-of-equilibrium systems is based on the local equilibrium hypothesis. However, the validity of the a priori assumption of local equilibrium has been questioned due to the…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…
A finite element method of any order is applied on a Bakhvalov-type mesh to solve a singularly perturbed convection--diffusion equation in 2D, whose solution exhibits exponential boundary layers. A uniform convergence of (almost) optimal…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
We present a novel staggered semi-implicit hybrid FV/FE method for the numerical solution of the shallow water equations at all Froude numbers on unstructured meshes. A semi-discretization in time of the conservative Saint-Venant equations…
In this study, we address the challenge of solving elliptic equations with quasiperiodic coefficients. To achieve accurate and efficient computation, we introduce the projection method, which enables the embedding of quasiperiodic systems…
In a range of physical systems, the first instability in Rayleigh-Bernard convection between nearly thermally insulating horizontal plates is large scale. This holds for thermal convection of fluids saturating porous media. Large-scale…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
Boiling is an extremely effective way to promote heat transfer from a hot surface to a liquid due to several mechanisms many of which are not understood in quantitative detail. An important component of the overall process is that the…
Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising…
Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modeling convection has given rise to the development of chaos theory…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
A low-dimensional model of large Prandtl-number ($P$) Rayleigh B\'{e}nard convection is constructed using some of the important modes of pseudospectral direct numerical simulations. A detailed bifurcation analysis of the low-dimensional…