Showing papers on "Incompressible flow published in 2007"
TL;DR: A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion, achieving second-order temporal accuracy and better than first-order spatial accuracy in L"2-norms for one- and two-dimensional test problems.
626 citations
TL;DR: The convective Cahn-Hilliard equation and the condition that the velocity field is divergence-free are derived from the conservation law of mass of binary mixtures in a straightforward way, for fluids with large density and viscosity ratios.
572 citations
TL;DR: To obtain sharp density and viscosity discontinuities in an incompressible multi- Phase SPH flow a new multi-phase projection formulation, in which the discretized gradient and divergence operators do not require a differentiable density or viscosities field is proposed.
459 citations
TL;DR: In this article, a discrete representation of the added mass operatorMA is given and ''instability conditions'' are evaluated for different temporal discretisation schemes and it is proven that for every sequentially staggered scheme and given spatial discretization of a problem, a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable.
453 citations
TL;DR: The new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant, thereby providing a speed-up over continuum or ''ghost-fluid'' methods.
389 citations
TL;DR: The results obtaining by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves indicates that the new methodology provides enhanced boundary layer resolution.
356 citations
TL;DR: The ability of the method to simulate flows with complex, moving immersed boundaries is applied to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.
353 citations
TL;DR: An immersed boundary method for time-dependent, three-dimensional, incompressible flows is presented, and the predictions show good agreement with previous computational and experimental results.
338 citations
TL;DR: An improved numerical algorithm for front tracking method is developed to simulate the rising of a bubble in quiescent viscous liquid due to buoyancy and predicted bubble shape and terminal velocity agree well with the experimental results.
317 citations
TL;DR: A sharp interface capturing method is described for the study of incompressible multiphase flows with phase change using the level set method to keep track of the interface between the two phases and a ghost fluid approach to impose the jump conditions at the interface.
313 citations
TL;DR: IFISS is a graphical Matlab package for the interactive numerical study of incompressible flow problems that includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions.
Abstract: IFISS is a graphical Matlab package for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions. The package can also be used as a computational laboratory for experimenting with state-of-the-art preconditioned iterative solvers for the discrete linear equation systems that arise in incompressible flow modelling. A unique feature of the package is its comprehensive nature; for each problem addressed, it enables the study of both discretization and iterative solution algorithms as well as the interaction between the two and the resulting effect on overall efficiency.
TL;DR: Some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation, are described in this paper.
Abstract: Euler equations of incompressible fluids use and enrich many branches of mathematics, from integrable systems to geometric analysis. They present important open physical and mathematical problems. Examples include the stable statistical behavior of ill-posed free surface problems such as the RayleighTaylor and Kelvin-Helmholtz instabilities. The paper describes some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation. Some of the recent results on the quasigeostrophic model are also mentioned.
TL;DR: In this article, the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow was analyzed for two boundary conditions: clamped-free and pinned-free.
TL;DR: A stabilized finite element approximation for the incompressible Navier–Stokes equations based on the subgrid-scale concept is analyzed and the properties of the discrete formulation that results allowing the sub grid-scales to depend on time are explored.
TL;DR: This paper uses the extended finite element space (XFEM), presented in [N. Moes, S. Usui, C. Parimi, Arbitrary discontinuities in finite elements], for the discretization of the pressure and shows that the size of spurious velocities is reduced substantially, provided the authors use both the new treatment of the surface tension force and the extended pressure finite elements space.
TL;DR: It is shown that both ''conservative'' and ''consistent'' are important properties of the scheme to get an accurate result for high Hartmann number MHD flows with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers of Hunt's conductive walls and Shercliff's insulated walls.
TL;DR: The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressed flows through porous media, and the continuity equation for porous media is considered inside obstacles.
TL;DR: In this article, an approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects.
Abstract: The approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure field from the experimental data, by making use of the flow constitutive equations. In this paper the implementation for two specific application areas is addressed. The first is time-mean pressure field and force evaluation from velocity ensemble statistics, as obtained from time-uncorrelated PIV acquisition, for incompressible flow. Two test cases are considered for this flow regime: the unsteady vortical flow around a square section cylinder at incidence, as well as the force characterization of a low-speed airfoil. The second topic considers the extension of the method to steady compressible flow, with the supersonic flow around a bi-convex airfoil as experimental test case. As in this flow regime the density appears as an extra unknown in the momentum equation, additional flow equations need to be invoked. A convenient approach for this was found, using the gas law and the adiabatic flow condition, with which the pressure-integration procedure becomes essentially the same as for the incompressible case.
TL;DR: An immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows is developed and validated for the Laplace relationship, the dispersion relationship for interfacial waves and the drag coefficient for cylinders.
Abstract: In this paper, we develop an immersed boundary lattice Boltzmann approach to simulate deformable capsules in flows. The lattice Boltzmann method is utilized to solve the incompressible flow field over a regular Eulerian grid, while the immersed boundary method is employed to incorporate the fluid–membrane interaction with a Lagrangian representation of the capsule membrane. This algorithm was validated for the Laplace relationship, the dispersion relationship for interfacial waves and the drag coefficient for cylinders; excellent agreement with theoretical results was observed. Furthermore, simulations of single and multiple red blood cells in shear and channel flows were performed. Several characteristic hemodynamic and hemorheological features were successfully reproduced, including the tank-treading motions, cell migration from the vessel wall, slipper-shaped cell deformation, cell-free layers, blunt velocity profiles and the Fahraeus effect. These simulations therefore demonstrate the potential usefulness of this computational model for microscopic biofluidic systems. However, extension of this algorithm to three-dimensional situations is necessary for more realistic simulations.
TL;DR: A novel immersed boundary velocity correction-lattice Boltzmann method is presented and validated in this work by its application to simulate the two-dimensional flow over a circular cylinder, which directly corrects the velocity to enforce the physical boundary condition.
TL;DR: A viscous vortex particle method is presented for computing the fluid dynamics of two-dimensional rigid bodies in motion, and the stability and convergence with respect to numerical parameters are explored in detail, with particular focus on the residual slip velocity.
TL;DR: In this paper, the authors consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele-Shaw cell.
Abstract: We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele–Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness when the smaller density is above (stable case) and in the unstable case we show ill-posedness.
TL;DR: Comparisons with the benchmark solutions for the two-dimensional driven cavity flow, thermal convection in a square box and flow past an impulsively started cylinder show that the high-order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary.
TL;DR: A smoothed particle hydrodynamic model for incompressible fluids that uses the SHAKE methodology familiar in constrained molecular dynamics as an efficient method for finding the non-thermodynamic pressure satisfying the constraints.
TL;DR: A finite element implementation of the standard κ-e turbulence model, including Chien's Low-Reynolds number modification is presented, with special emphasis on the numerical treatment of wall boundary conditions.
Abstract: A finite element implementation of the standard κ-e turbulence model, including Chien's Low-Reynolds number modification is presented. Special emphasis is laid on the numerical treatment of wall boundary conditions. In particular, logarithmic wall functions are used to derive Neumann boundary conditions for the standard κ-e model. The resulting solutions are superior to those obtained using wall functions implemented as Dirichlet boundary conditions and comparable to simulation results produced by a Low-Reynolds number κ-e model. Two representative benchmark problems (channel flow and backward facing step) are used to compare the performance of different algorithms in 3D and to investigate the influence of the near-wall treatment.
TL;DR: In this article, a non-physical velocity may appear in the finite element calculation of incompressible two-phase flows subjected to an external local force, and this velocity does not vanish with the expected order of convergence.
TL;DR: Numerical experiments indicate that the first-order versions of the two Gauge-Uzawa schemes lead to first- order convergence rate for all variables and that these schemes are suitable for handling problems with large density ratios such as in the situation of air bubble rising in water.
TL;DR: Mathematical modeling and analytical solution are presented for the flow of an incompressible Carreau fluid in an asymmetric channel with sinusoidal wall variations.
TL;DR: An interface tracking method using an unstructured moving mesh has been developed for simulating three-dimensional, incompressible, and immiscible two-phase flows and is found to be in excellent agreement with analytical solutions and experimental results.
TL;DR: In this paper, the authors present 2D and 3D upper bound solutions for the problem of tunnel excavation in soft ground, which invokes the use of incompressible flow fields derived from the theory of elasticity and the concept of sinks and sources.
Abstract: This paper presents 2D and 3D upper bound solutions for the problem of tunnel excavation in soft ground. The solution invokes the use of incompressible flow fields derived from the theory of elasticity and the concept of sinks and sources. Comparison is made with previously published results. For some geometries the current calculation results in lower (better) upper bound values; however, the results were generally close to previously published values.