The goal of this article is to contribute to a more precise discussion of the question whether Lattice-Boltzmann (LB) methods can be regarded as efficient CFD solvers. After a short review of the basic model and recommendable extensions, we compare the accuracy and computational efficiency of two research simulation codes based on the LB and the Finite-Element method (FEM) for incompressible la...

1 Abstract The role of vorticity dynamics in vortex breakdown is examined in a theoretical and computational study. Under the assumptions of steady, incompressible, axisymmetric, invis-cid ow, a theory is developed concerning the interaction of vortex tilting and stretching in the breakdown process. This analytic theory is then connrmed using an unsteady, incompressible, axisymmetric viscous ow...

The distribution of electron density in the quantum Hall liquid is considered in the presence of macroscopic density gradient caused by side electrodes or inhomogeneous doping. In this case different Landau levels are occupied in different regions of a sample. These regions are separated by “incompressible liquid”. It is shown that the applicability of the approach by Chklovskii et al. is subst...

The simplifications required to apply the Boussinesq approximation to compressible flow are compared with those in an incompressible fluid. The larger degree of approximation required to describe mass conservation in a stratified compressible fluid with the Boussinesq continuity equation has led to the development of several different sets of “anelastic” equations that may be regarded as genera...

We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solid-fluid coupling. Ther...

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite and spectral element methods with discontinuous pressures. Two different approaches are considered to solve the resulting saddle point systems: a) a precondit...

In this paper a Godunov-type projection method for computing approximate solutions of the zero Froude number (incompressible) shallow water equations is presented. It is second-order accurate and locally conserves height (mass) and momentum. To enforce the underlying divergence constraint on the velocity field, the predicted numerical fluxes, computed with a standard second order method for hyp...

The projection method is a widely used fractional-step algorithm for solving the incompressible Navier–Stokes equations. Despite numerous improvements to the methodology, however, imposing physical boundary conditions with projection-based fluid solvers remains difficult, and obtaining high-order accuracy may not be possible for some choices of boundary conditions. In this work, we present an u...

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under fi...

Incompressible interfacial ows here refer to those incompressible ows possessing multiple distinct, immiscible uids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface ows, where uid properties across the interface vary by orders of magnitude. Interfaces present in these ows possess topologies that are not only irregular but also dynamic, undergoing g...