In incompressible flows with vanishing normal velocities at the boundary, irrotational forces in the momentum equations should be balanced completely by the pressure gradient. Unfortunately, nearly all available discretization methods for incompressible flows violate this property. The origin of the problem is that discrete velocity approximations of incompressible flows are usually not diverge...

We introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem, in two and three dimensions. The velocity field is discretized using divergence-conforming Brezzi-Douglas-Marini (BDM) elements and the magnetic field is approximated by curl-conforming Nédélec elements. The H1-continuity of the velocity field is e...

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

Abstract. This work presents and analyzes a new Residual Local Projection stabilized finite element method (RELP) for the non-linear incompressible Navier–Stokes equations. Stokes problems defined element–wisely drive the construction of the residual-based terms which make the present method stable for the finite element pairs P1/Pl, l = 0, 1. Numerical upwinding is incorporated through an extr...

Geometric dispersion is commonly observed in shallow water marine data due to post-critical multiples in the water layer over a hard seafloor. Characteristics of the guided waves include formation of distinct propagation modes and associated divergence of phase and group velocity. Methods have been available since 1981 to image phase velocity dispersion curves. Here we report a method to direct...

Free Surface Test (2D).. Our free surface Stokes test case is a fluid disk of radius r = 0.75 centred at the origin, with density ρ = 1 and viscosity μ = 0.1, computed over a timestep ∆t = 1 . For simplicity of presentation, we describe the final velocity field in terms of a stream function,ψ , where the velocity field can be derived as uf inal = ∇ ×ψ . This also guarantees that the velocity fi...

PURPOSE The purpose of this study was to investigate the relationship between phoria and the dynamics of vergence eye movements as described by the ratio of convergence average peak velocity to divergence average peak velocity, termed the vergence peak velocity ratio. METHODS Phoria and vergence step responses were recorded. Three measures of phoria were assessed: baseline phoria, which is th...

In this paper we study homogenization of nonlinear hyperbolic equations. The weak limit of the solutions is investigated by approximating the flux functions with piecewise linear functions. We study mostly Riemann problems for layered velocity fields as well as for the heterogeneous divergence free velocity fields.

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms ...

We propose a method for measuring the cosmological density parameter from the statistics of the expansion scalar, H 1 r v, { the divergence of peculiar velocity, expressed in units of the Hubble constant, H 100h km s 1 Mpc 1 . The velocity eld is spatially smoothed over 10h 1 Mpc to remove strongly nonlinear e ects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial uctuati...