Results 1  10
of
91
Gerris: A TreeBased Adaptive Solver For The Incompressible Euler Equations In Complex Geometries
 J. Comp. Phys
, 2003
"... An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Sec ..."
Abstract

Cited by 100 (16 self)
 Add to MetaCart
An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Secondorder convergence in space and time is demonstrated on regular, statically and dynamically refined grids. The quad/octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features. The source code of the method implementation is freely available.
A sharp interface Cartesian grid method for simulating flows with complex moving boundaries
 J. Comput. Phys
, 2001
"... A Cartesian grid method for computing flows with complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. A mixed Eulerian– Lagrangian framework is employed, which allows us to treat the imm ..."
Abstract

Cited by 66 (4 self)
 Add to MetaCart
(Show Context)
A Cartesian grid method for computing flows with complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. A mixed Eulerian– Lagrangian framework is employed, which allows us to treat the immersed moving boundary as a sharp interface. The incompressible Navier–Stokes equations are discretized using a secondorderaccurate finitevolume technique, and a secondorderaccurate fractionalstep scheme is employed for time advancement. The fractionalstep method and associated boundary conditions are formulated in a manner that properly accounts for the boundary motion. A unique problem with sharp interface methods is the temporal discretization of what are termed “freshly cleared ” cells, i.e., cells that are inside the solid at one time step and emerge into the fluid at the next time step. A simple and consistent remedy for this problem is also presented. The solution of the pressure Poisson equation is usually the most timeconsuming step in a fractional step scheme and this is even more so for moving boundary problems where the flow domain changes constantly. A multigrid method is presented and is shown to
An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries
 J. Comp. Phys
, 2006
"... We present an immersed interface method for the incompressible NavierStokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the noslip condition on the boundary is satisfied, singular fo ..."
Abstract

Cited by 37 (3 self)
 Add to MetaCart
(Show Context)
We present an immersed interface method for the incompressible NavierStokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the noslip condition on the boundary is satisfied, singular forces are applied on the fluid. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of the singular forces is determined by solving a small system of equations iteratively at each time step. The NavierStokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity. Keywords: Immersed interface method, NavierStokes equations, Cartesian grid method, finite difference, fast Poisson solvers, irregular domains.
Immersed boundary technique for turbulent flow simulations
 Appl. Mech. Rev
"... The application of the Immersed Boundary ͑IB͒ method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of nonbody conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equ ..."
Abstract

Cited by 33 (2 self)
 Add to MetaCart
The application of the Immersed Boundary ͑IB͒ method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of nonbody conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard ReynoldsAveraged NavierStokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references. ͓DOI: 10.1115/1.1563627͔ CONTEXT The continuous growth of computer power strongly encourages engineers to rely on computational fluid dynamics ͑CFD͒ for the design and testing of new technological solutions. Numerical simulations allow the analysis of complex phenomena without resorting to expensive prototypes and difficult experimental measurements. The basic procedure to perform numerical simulation of fluid flows requires a discretization step in which the continuous governing equations and the domain of interest are transformed into a discrete set of algebraic relations valid in a finite number of locations ͑computational grid nodes͒ inside the domain. Afterwards, a numerical procedure is invoked to solve the obtained linear or nonlinear system to produce the local solution to the original equations. This process is simple and very accurate when the grid nodes are distributed uniformly ͑Cartesian mesh͒ in the domain, but becomes computationally intensive for disordered ͑unstructured͒ point distributions. For simple computational domains ͑a box, for example͒ the generation of the computational grid is trivial; the simulation of a flow around a realistic configuration ͑a road vehicle in a wind tunnel, for example͒, on the other hand, is extremely complicated and time consuming since the shape of the domain must include the wetted surface of the geometry of interest. The first difficulty arises from the necessity to build a smooth surface mesh on the boundaries of the domain ͑body conforming grid͒. Usually industrially relevant geometries are defined in a CAD environment and must be translated and cleaned ͑small details are usually eliminated, overlapping surface patches are trimmed, etc͒ before a surface grid can be generated. This mesh serves as a starting point to generate the volume grid in the computational domain. In addition, in many industrial applications, geometrical complexity is combined with moving boundaries and high Reynolds numbers. This requires regeneration or deformation of the grid during the simulation and turbulence modeling, leading to a considerable increase of the computational difficulties. As a result, engineering flow simulations have large computational overhead and low accuracy owing to a large number of operations per node and high storage requirements in combination with low order dissipative spatial discretization. Given the finite memory and speed of computers, these simulations are very expensive and time consuming with computational meshes that are generally limited to around one million nodes. In view of these difficulties, it is clear that an alternative numerical procedure that can handle the geometric complexity, but at the same time retains the accuracy and high efficiency of the simulations performed on regular grids, would represent a significant advance in the application of CFD to industrial flows.
A Cartesian grid method for solving the twodimensional streamfunctionvorticity equations in irregular regions
 J. Comput. Phys
"... We describe a method for solving the twodimensional Navier–Stokes equations in irregular physical domains. Our method is based on an underlying uniform Cartesian grid and secondorder finitedifference/finitevolume discretizations of the streamfunctionvorticity equations. Geometry representing st ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
(Show Context)
We describe a method for solving the twodimensional Navier–Stokes equations in irregular physical domains. Our method is based on an underlying uniform Cartesian grid and secondorder finitedifference/finitevolume discretizations of the streamfunctionvorticity equations. Geometry representing stationary solid obstacles in the flow domain is embedded in the Cartesian grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells. Along the embedded boundary, we determine a distribution of vorticity sources needed to impose the noslip flow conditions. This distribution appears as a righthandside term in the discretized fluid equations, and so we can use fast solvers to solve the linear systems that arise. To handle the advective terms, we use the highresolution algorithms in CLAWPACK. We show that our Stokes solver is secondorder accurate for steady state solutions and that our full Navier–Stokes solver is between first and secondorder accurate and reproduces results from wellstudied benchmark problems in viscous fluid flow. Finally, we demonstrate the robustness of our code on flow in
Numerical Methods for FluidStructure Interaction  A Review
, 2012
"... The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming me ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
The interactions between incompressible fluid flows and immersed structures are nonlinear multiphysics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical methods based on conforming and nonconforming meshes that are currently available for computing fluidstructure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluidstructure interactions.
Formation criterion for synthetic jets
 AIAA journal
"... A formation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zeronet massflux device that imparts momentum to its surroundings. Jet formation is defined as the appearance of a timeaveraged outward velocity along the jet axis and corresponds to the generation a ..."
Abstract

Cited by 20 (2 self)
 Add to MetaCart
A formation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zeronet massflux device that imparts momentum to its surroundings. Jet formation is defined as the appearance of a timeaveraged outward velocity along the jet axis and corresponds to the generation and subsequent convection or escape of a vortex ring. It is shown that over a wide range of operating conditions synthetic jet formation is governed by the jet Strouhal number Sr (or Reynolds number Re and Stokes number S). Both numerical simulations and experiments are performed to supplement available twodimensional and axisymmetric synthetic jet formation data in the literature. The data support the jet formation criterion 1/Sr = Re/S2> K, where the constant K is approximately 1 and 0.16 for twodimensional and axisymmetric synthetic jets, respectively. In addition, the dependence of the constant K on the normalized radius of curvature of a rounded orifice or slot is addressed. The criterion is expected to serve as a useful design guide for synthetic jet formation in flow control, heat transfer, and acoustic liner applications, in which a stronger jet is synonymous with increased momentum transfer, vorticity generation, and acoustic nonlinearities. I.
A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered threedimensional Cartesian grid
, 2003
"... ..."