Related papers: Structure-Preserving Discretization of Incompressi…
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative…
Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…
Conserved or dissipated quantities, like energy or entropy, are at the heart of the study of many classes of time-dependent PDEs in connection with fluid mechanics. This is the case, for instance, for the Euler and Navier-Stokes equations,…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
We propose an efficient semi-Lagrangian Characteristic Mapping (CM) method for solving the three-dimensional (3D) incompressible Euler equations. This method evolves advected quantities by discretizing the flow map associated with the…
Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…
Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a…
We develop a rigorous theory for a structure-preserving discretisation of the incompressible Euler and Navier--Stokes equations, based on discrete exterior calculus on prismatic Delaunay--Voronoi meshes over closed Riemannian manifolds. The…
By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is…
This paper proposes a hierarchy of numerical fluxes for the compressible flow equations which are kinetic-energy and pressure equilibrium preserving and asymptotically entropy conservative, i.e., they are able to arbitrarily reduce the…
Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the curl or the divergence of a vector that appear as an implicit constraint. In this article, we…
The Lagrangian average (LA) of the ideal fluid equations preserves their transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its convection of potential vorticity…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
We formulate the equations of fluid dynamics as an intersection-theoretic problem on an infinite-dimensional symplectic manifold naturally associated with spacetime. This perspective separates the structures determined by the equation of…
In this study, we demonstrate that an inviscid fluid in a near-equilibrium state, when viewed in the Lagrangian picture in d+1 spacetime dimensions, can be reformulated as a (d-1)-form gauge theory. We construct a fluid/p-form dictionary…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc Roy Soc, 2013). These models have a Kelvin circulation theorem that holds on all materially-transported closed loops, not just those loops…
We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's equations of inviscid incompressible fluids. The method…