Showing papers on "Incompressible flow published in 2010"
Book•
26 Jul 2010TL;DR: In this article, the Laplace and Stokes equations were used to model the fluid and current flow in molecular-scale and thick-double-layer systems and the dynamics of diffuse charge.
Abstract: 1. Kinematics, conservation equations, and boundary conditions for incompressible flow 2. Unidirectional flow 3. Hydraulic circuit analysis 4. Passive scalar transport: dispersion, patterning, and mixing 5. Electrostatics and electrodynamics 6. Electroosmosis 7. Potential fluid flow 8. Stikes flow 9. The diffuse structure of the electrical double layer 10. Zeta potential in microchannels 11. Species and charge transport 12. Microchip chemical separations 13. Particle electrophoresis 14. DNA transport and analysis 15. Nanofluidics: fluid and current flow in molecular-scale and thick-double-layer systems 16. AC electrokinetics and the dynamics of diffuse charge 17. Particle and droplet actuation: dielectrophoresis, magnetophoresis, and digital microfluidics Appendices: A. Units and fundamental constants B. Properties of electrolyte solutions C. Coordinate systems and vector calculus D. Governing equation reference E. Nondimensionalization and characteristic parameters F. Multipolar solutions to the Laplace and Stokes equations G. Complex functions H. Interaction potentials: atomistic modeling of solvents and solutes.
898 citations
TL;DR: In this article, a model for the flow of a mixture of two homogeneous and incompressible fluids in a two-dimensional bounded domain is considered, where the model consists of a Navier-Stokes equation governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids.
Abstract: We consider a model for the flow of a mixture of two homogeneous and incompressible fluids in a two-dimensional bounded domain. The model consists of a Navier–Stokes equation governing the fluid velocity coupled with a convective Cahn–Hilliard equation for the relative density of atoms of one of the fluids. Endowing the system with suitable boundary and initial conditions, we analyze the asymptotic behavior of its solutions. First, we prove that the initial and boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses the global attractor A . Then we establish the existence of an exponential attractors E . Thus A has finite fractal dimension. This dimension is then estimated from above in terms of the physical parameters. Moreover, assuming the potential to be real analytic and in absence of volume forces, we demonstrate that each trajectory converges to a single equilibrium. We also obtain a convergence rate estimate in the phase-space metric.
226 citations
TL;DR: The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow.
160 citations
TL;DR: The present implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier-Stokes equations is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.
145 citations
TL;DR: In this paper, a new theory of exact particle flow for nonlinear filters is proposed, which generalizes our theory of particle flow that is already many orders of magnitude faster than the standard particle filters and which is several order of magnitude more accurate than the extended Kalman filter for difficult nonlinear problems.
Abstract: We have invented a new theory of exact particle flow for nonlinear filters. This
generalizes our theory of particle flow that is already many orders of magnitude faster than
standard particle filters and which is several orders of magnitude more accurate than the
extended Kalman filter for difficult nonlinear problems. The new theory generalizes our recent
log-homotopy particle flow filters in three ways: (1) the particle flow corresponds to the exact flow
of the conditional probability density; (2) roughly speaking, the old theory was based on
incompressible flow (like subsonic flight in air), whereas the new theory allows compressible flow
(like supersonic flight in air); (3) the old theory suffers from obstruction of particle flow as well as
singularities in the equations for flow, whereas the new theory has no obstructions and no
singularities. Moreover, our basic filter theory is a radical departure from all other particle filters in
three ways: (a) we do not use any proposal density; (b) we never resample; and (c) we compute
Bayes' rule by particle flow rather than as a point wise multiplication.
140 citations
TL;DR: A more efficient approach to solve lattice Boltzmann equation on the non-uniform Cartesian mesh needs much less computational time and virtual storage and can be applied to simulate three-dimensional incompressible viscous flows.
131 citations
TL;DR: A conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid, suitable for Large-Eddy Simulations of high-Reynolds number flows.
122 citations
TL;DR: The LS-STAG method is presented, which is based on the MAC method for staggered Cartesian grids and where the irregular boundary is sharply represented by its level-set function, and achieves a novel discretization of the fluxes in the cut-cells by enforcing the strict conservation of total mass, momentum and kinetic energy at the discrete level.
114 citations
TL;DR: In this paper, a detailed numerical investigation of turbulent liquid jets in quiescent air is conducted, with the focus on the processes leading to liquid atomization, and Spectral refinement of the interface is employed to provide an accurate description of the phase interface, even at the subcell level.
Abstract: A detailed numerical investigation of turbulent liquid jets in quiescent air is conducted, with the focus on the processes leading to liquid atomization. Spectral refinement of the interface is employed to provide an accurate description of the phase interface, even at the subcell level. The ghost fluid method is used to handle the different material properties of the phases and the surface tension force in a sharp manner. A temporally evolving turbulent planar jet is simulated for several values of the Reynolds and Weber numbers, and statistics are extracted. Direct visualization of the flow structures allows one to lay out a clear picture of the atomization process. Early interface deformation is caused by turbulent eddies that carry enough kinetic energy to overcome surface tension forces. Then, liquid protrusions are stretched out into ligaments that rupture following Rayleigh’s theory or due to aerodynamic forces. This numerical study provides a wealth of much-needed detailed information on the turbulent atomization process, which is invaluable to large eddy simulation modeling.
96 citations
TL;DR: In this article, a blow-up criterion for classical solutions to the 3D compressible Navier-Stokes equations was proposed, analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow.
Abstract: In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier- Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, the initial vacuum is allowed in our case. MSC(2000): 76N10
95 citations
DOI•
01 Jan 2010
TL;DR: A novel boundary handling scheme for incompressible fluids based on Smoothed Particle Hydrodynamics (SPH) is presented and an adaptive time-stepping approach is proposed that automatically estimates appropriate time steps independent of the scenario.
Abstract: We present a novel boundary handling scheme for incompressible fluids based on Smoothed Particle Hydrodynamics (SPH). In combination with the predictive-corrective incompressible SPH (PCISPH) method, the boundary handling scheme allows for larger time steps compared to existing solutions. Furthermore, an adaptive time-stepping approach is proposed. The approach automatically estimates appropriate time steps independent of the scenario. Due to its adaptivity, the overall computation time of dynamic scenarios is significantly reduced compared to simulations with constant time steps.
TL;DR: A novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.
TL;DR: In this article, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem, and numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively.
TL;DR: A structured adaptive mesh refinement strategy for fluid-structure interaction problems in laminar and turbulent incompressible flows and an embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines.
TL;DR: A dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media based on moving particle semi-implicit (MPS) method that is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples.
TL;DR: In this article, an alternative method is presented that linearizes the hydrodynamic load of a rigid, oscillating hydrofoil, which is modeled with forced and free pitching motions, where the mean incidence angle is 0° with a maximum angle amplitude of 2°.
TL;DR: In this article, the existence and uniqueness of the global strong solution with small initial data are established, and it is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution.
Abstract: The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution.
TL;DR: This work devise new higher-order accurate time-discrete projection methods that extend a slip-correction idea behind the well-known finite-difference scheme of Kim and Moin and test these schemes for stability and accuracy using various combinations of C^0 finite elements.
TL;DR: In this paper, a diffuse interface model for the evolution of an incompressible two-phase flow in a two-dimensional bounded domain is considered, which consists of the Navier-Stokes equation for the fluid velocity u coupled with a convective Allen-Cahn equation for u, both endowed with suitable boundary conditions.
Abstract: We consider a diffuse interface model for the evolution of an
iso-thermal incompressible two-phase flow in a two-dimensional bounded
domain. The model consists of the Navier-Stokes equation for the fluid
velocity u coupled with a convective Allen-Cahn equation for
the order (phase) parameter $\phi$, both endowed with suitable boundary
conditions. We analyze the asymptotic behavior of the solutions within the
theory of infinite-dimensional dissipative dynamical systems. We first prove
that the initial and boundary value problem generates a strongly continuous
semigroup on a suitable phase space which possesses the global attractor $
\mathcal{A}$. Then we establish the existence of an exponential attractor $
\mathcal{E}$ which entails that $\mathcal{A}$ has finite fractal dimension.
This dimension is then estimated in terms of some model parameters.
Moreover, assuming the potential to be real analytic, we demonstrate that,
in absence of external forces, each trajectory converges to a single
equilibrium by means of a Łojasiewicz-Simon inequality. We also obtain a
convergence rate estimate. Finally, we discuss the case where $\phi $ is
forced to take values in a bounded interval, e.g., by a so-called singular
potential.
TL;DR: In this paper, the authors present a precise definition of numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows, which is physically reasonable as the coarse and fine scales are properly separated.
TL;DR: The code validation shows that the proposed interface reconstruction scheme can be employed to resolve complex interface changes efficiently and accurately and can be used directly in near-interface sub-grid models in large eddy simulation.
TL;DR: A massively parallel high-order Navier-Stokes solver for large incompressible flow problems in three dimensions that uses a highly efficient commutation-based preconditioner and investigates the absolute accuracy of the implementation with respect to the different termination criteria.
TL;DR: In this paper, a simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales for the dynamical situation of a gravity wave (GW) near breaking level, and the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic GWs.
Abstract: Multiple-scale asymptotics is used to analyse the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As a small expansion parameter, the ratio of the inverse of the vertical wavenumber and potential temperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudo-incompressible equations, both for non-hydrostatic and hydrostatic GWs, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak stratification is adopted. To describe vertical propagation of wavepackets over several atmospheric-scale heights, Wentzel–Kramers–Brillouin (WKB) theory is used to show that the pseudo-incompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justification for the use of the pseudo-incompressible equations in the study of GW breaking in the atmosphere for arbitrary background stratification. The WKB theory interestingly even holds at wave amplitudes close to static instability. In the mean-flow equations, we obtain in addition to the classic wave-induced momentum-flux divergences a wave-induced correction of hydrostatic balance in the vertical momentum equation, which cannot be obtained from Boussinesq or anelastic dynamics.
TL;DR: Numerical tests for different type of boundary layers arising in convection–diffusion problems illustrate the stabilizing properties of the method.
Abstract: We give a survey on recent developments of stabilization methods based on local projection type. The considered class of problems covers scalar convection–diffusion equations, the Stokes problem and the linearized Navier–Stokes equations. A new link of local projection to the streamline diffusion method is shown. Numerical tests for different type of boundary layers arising in convection–diffusion problems illustrate the stabilizing properties of the method.
TL;DR: In this paper, the authors used matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm to solve linear systems that arise in incompressible flow computations.
Abstract: Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid–structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm. It is well known that solving linear systems that arise in incompressible flow computations consume most of the time required by such simulations. For solving these large sparse nonsymmetric systems, we present effective preconditioning techniques appropriate for different stages of the computation over a cardiac cycle.
TL;DR: This work proposes a modification of the P 1 -conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system.
TL;DR: In this article, a numerical model for the simulation of incompressible two-phase flows of a flat granular bed submitted to a laminar shearing flow is presented, considering a two-fluid model and a mixedfluid one, where the governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint.
TL;DR: In this article, a stress power-law model is proposed to express the kinematic quantities in terms of the stress of the velocity gradient, which can be used as a substitute for the classical power law models.
TL;DR: In this paper, a more efficient algorithm for Lagrangian moving particles is used for solving various highly nonlinear free-surface problems without using the Eulerian approach or the grid system.