Download or read book Numerical Investigation on the Projection Method for the Incompressible Navier Stokes Equations on MAC Grid written by Vorleak Yek and published by . This book was released on 2018 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A MAC Grid Based Multigrid Solver for the Incompressible Navier Stokes Equations with Immersed Boundaries written by Matthew Dean Winger (Graduate student) and published by . This book was released on 2020 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Projection and Quasi Compressibility Methods for Solving the Incompressible Navier Stokes Equations written by and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Numerical Resolution of the Incompressible Navier Stokes Equations written by Mardan Sajjad and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2001 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis written by Society for Industrial and Applied Mathematics and published by . This book was released on 1999-07 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1989 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Resolution Methods for Incompressible and Low Speed Flows written by D. Drikakis and published by Springer Science & Business Media. This book was released on 2005-08-02 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Numerical Method for the Incompressible Navier Stokes Equations Based on an Approximate Projection written by Ann S. Almgren and published by . This book was released on 1993 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Study of a Multigrid Method with Four Smoothing Methods for the Incompressible Navier Stokes Equations in General Coordinates written by S. Zeng and published by . This book was released on 1993 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Evaluation of a Multigrid Scheme for the Incompressible Navier Stokes Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-05-31 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.Swanson, R. C.Langley Research CenterMULTIGRID METHODS; NAVIER-STOKES EQUATION; INCOMPRESSIBLE FLOW; AIRFOILS; TREFFTZ METHOD; RUNGE-KUTTA METHOD; REYNOLDS NUMBER; PARABOLAS; FLAT PLATES; CONVERGENCE; ALGORITHMS

Download or read book Numerical Solutions of the Navier Stokes Equations for Incompressible Uniform Flow Past a Parabola written by Earnest Wade Miner and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solving the navier stokes equations using an exact projection method on a 2 D staggered grid written by and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solutions of the Navier Stokes Equations for Incompressible Uniform Flow Past a Parabola written by William C. Boswell and published by . This book was released on 1971 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical solutions are obtained to the Navier-Stokes equations for the problem of flow past a parabolic cylinder in an infinite stream. The boundary conditions at infinity have been applied at finite distances and the effects studied and compared with recent works. It was found that finite boundaries had small, but noticeable effects on the wall shear, and more marked influence on the internal flow structure. (Author).

Download or read book Numerical Solutions of the Navier Stokes Equations for Incompressible Uniform Flow Past a Parabola a Study of Finite Grid Size Effects by W C Boswell Jr and M J Werle written by W C. Boswell and published by . This book was released on with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Chorin s Projection Method for the Incompressible Navier Stokes Equations written by R. Rannacher and published by . This book was released on 1991 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: