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The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
The aim of this paper is to discuss several aspects of connections between the p-Laplacian and mathematical models in hydrology. At first we present models of groundwater flow in phreatic aquifers and models of irrigation and drainage that…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
The relationship between computational models and dynamics has captivated mathematicians and computer scientists since the earliest conceptualizations of computation. Recently, this connection has gained renewed attention, fueled by T.…
How useful it is to think about the potential energy landscape of a complex many-body system depends in large measure on how direct the connection is to the system's dynamics. In this paper we show that, within what we call the potential…
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
We report on a new methodological approach to electrodynamics based on a fluidic viewpoint. We develop a systematic approach establishing analogies between physical magnitudes and isomorphism (structure-preserving mappings) between systems…
We use a general circulation model to study the three-dimensional (3-D) flow and temperature distributions of atmospheres on tidally synchronized extrasolar planets. In this work, we focus on the sensitivity of the evolution to the initial…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
The application of principles of thermodynamics and statistical mechanics to economic systems is considered in a broad historical perspective, extending from prehistoric times to the present day. The hypothesis of maximum entropy production…
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally…
The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
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…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
A computational fluid dynamics (CFD) model that solves the steady-state Reynolds-Averaged Navier-Stokes (RANS) equations for buoyant compressible pollution dispersion under different meteorological conditions is developed. A 6.4 km by 6.4…
Environmental fluid mechanics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that…