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Author: Vorleak Yek Publisher: ISBN: 9780438258624 Category : Fluid dynamics Languages : en Pages : 76
Book Description
Abstract: The motion of a viscous fluid flow is described by the well-known Navier-Stokes equations. The Navier-Stokes equations contain the conservation laws of mass and momentum, and describe the spatial-temporal change of the fluid velocity field. This thesis aims to investigate numerical solvers for the incompressible Navier-Stokes equations in two and three space dimensions. In particular, we focus on the second-order projection method introduced by Kim and Moin, which was extended from Chorin’s first-order projection method. We apply Fourier-Spectral methods for the periodic boundary condition. Numerically, we discretize the system using central differences scheme on Marker and Cell (MAC) grid spatially and the Crank-Nicolson scheme temporally. We then apply the fast Fourier transform to solve the resulting Poisson equations as sub-steps in the projection method. We will verify numerical accuracy and provide the stability analysis using von Neumann. In addition, we will simulate the particles' motion in the 2D and 3D fluid flow.
Author: Vorleak Yek Publisher: ISBN: 9780438258624 Category : Fluid dynamics Languages : en Pages : 76
Book Description
Abstract: The motion of a viscous fluid flow is described by the well-known Navier-Stokes equations. The Navier-Stokes equations contain the conservation laws of mass and momentum, and describe the spatial-temporal change of the fluid velocity field. This thesis aims to investigate numerical solvers for the incompressible Navier-Stokes equations in two and three space dimensions. In particular, we focus on the second-order projection method introduced by Kim and Moin, which was extended from Chorin’s first-order projection method. We apply Fourier-Spectral methods for the periodic boundary condition. Numerically, we discretize the system using central differences scheme on Marker and Cell (MAC) grid spatially and the Crank-Nicolson scheme temporally. We then apply the fast Fourier transform to solve the resulting Poisson equations as sub-steps in the projection method. We will verify numerical accuracy and provide the stability analysis using von Neumann. In addition, we will simulate the particles' motion in the 2D and 3D fluid flow.
Author: Matthew Dean Winger (Graduate student) Publisher: ISBN: Category : Computational fluid dynamics Languages : en Pages : 37
Book Description
Abstract: For this work, two-dimensional fluid dynamics within an enclosed square domain are simulated using the incompressible Navier-Stokes equations. The computational domain is discretized using the Marker-And-Cell (MAC) method which places velocity and pressure components in a mesh of staggered grids, offering improved solution stability as opposed to placing these components on the same grid. A modified form of the projection method is used to linearize the incompressible equations which produces a series of systems which are solved for velocity and pressure. With an immersed boundary method we can simulate the effect various surfaces with no-slip boundary conditions have on the fluid flow when placed inside our domain via a forcing term which is added to our systems. Solution of these linear systems is achieved by using the multigrid method, which uses restriction and interpolation operators that account for the staggered grids produced by the MAC method. With these tools we are able to describe a variety of types of fluid simulations, illustrated in this work with a series of numerical examples.
Author: Publisher: Springer Science & Business Media ISBN: 3663111717 Category : Technology & Engineering Languages : en Pages : 302
Book Description
Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor
Author: Mardan Sajjad Publisher: ISBN: Category : Languages : en Pages :
Book Description
This thesis is aimed at solvingNavier-Stokes equation using Fractional Step Method also known as MAC method using staggered grids.Study was extended on deep study and researching about different schemes of higher order and how to improve the accuracy of solution to convection-diffusionequation by using high order schemes with and without flux limiters. Different schemes from literature has been described in this thesis. For comparison and validation of theory two different cases were tested Driven SMITH-HUTTON or Solenoidal flow problem and Diagonal flow problem for different mesh size are tested using own assembled MATLAB code.A separate code was prepared to model the Solution 2-dimensional solution to Incompressible Navier-Stokes Equations, by presenting a benchmark problem of LID-Driven Cavity.The most expensive task in the code is the solution to linear equations hence, solvers were used and discussed different solver to determine the most efficient one. Finite Volume Method has been implemented to study solution to this convection-diffusion equation.
Author: D. Drikakis Publisher: Springer Science & Business Media ISBN: 354026454X Category : Science Languages : en Pages : 623
Book Description
The study of incompressible ?ows is vital to many areas of science and te- nology. This includes most of the ?uid dynamics that one ?nds in everyday life from the ?ow of air in a room to most weather phenomena. Inundertakingthesimulationofincompressible?uid?ows,oneoftentakes many issues for granted. As these ?ows become more realistic, the problems encountered become more vexing from a computational point-of-view. These range from the benign to the profound. At once, one must contend with the basic character of incompressible ?ows where sound waves have been analytically removed from the ?ow. As a consequence vortical ?ows have been analytically “preconditioned,” but the ?ow has a certain non-physical character (sound waves of in?nite velocity). At low speeds the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows are governed by a balance between the inertial and viscous forces in the ?ow that provides the stability. Flows are often characterized by a dimensionless number known as the Reynolds number, which is the ratio of inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller Reynolds numbers. Even though laminar ?ows are organized in an orderly manner, the ?ows may exhibit instabilities and bifurcation phenomena which may eventually lead to transition and turbulence. Numerical modelling of suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight into the relationship of the numerical methods with the ?ow physics.
Author: Vorleak Yek
Author: Vorleak Yek
Author: Matthew Dean Winger (Graduate student)
Author: 
Author: Mardan Sajjad
Author: 
Author: Society for Industrial and Applied Mathematics
Author: D. Drikakis
Author: 
Author: Ann S. Almgren
Author: S. Zeng