Related papers: Complex Variable Methods for 3D Applied Mathematic…
This paper investigates the existence and uniqueness of local strong solutions to the three-dimensional compressible magnetohydrodynamic (MHD) equations with density-dependent viscosities in an exterior domain. The system models the…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and…
Our understanding of the material organization of complex fluid flows has recently benefited from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify…
Turbulent flows are fundamental in engineering and the environment, but their chaotic and three-dimensional (3-D) nature makes them computationally expensive to simulate. In this work, a dimensionality reduction technique is investigated to…
This research explores the development and application of the High-Order Dynamic Integration Method for solving integro-differential equations, with a specific focus on turbulent fluid dynamics. Traditional numerical methods, such as the…
We consider inverse problems related to the velocity reconstruction in electrically conducting fluids from externally measured magnetic fields. The underlying theory is presented in the framework of the integral equation approach to…
An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety…
In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E \textbf{92}, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it…
In the article the authors present a numerical method for modelling a laminar-turbulent transition in magnetohydrodynamic flows. The equations in the small magnetic Reynolds numbers approach is considered. Speed, pressure and electrical…
In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid motion. In this paper, we develop a novel numerical method…
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…
The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
We consider possible generation of singularities of a vector field transported by diffeomorphisms with derivatives of uniformly bounded determinants. A particular case of volume preserving diffeomrphism is the most important, since it has…