3 edition of **A multidomain spectral collocation method for the Stokes problem** found in the catalog.

A multidomain spectral collocation method for the Stokes problem

G. Sacchi Landriani

- 205 Want to read
- 36 Currently reading

Published
**1989**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
.

Written in English

- Collocation.,
- Decomposition.,
- Divergence.,
- Domains.,
- Stokes theorem (Vector calculus)

**Edition Notes**

Statement | G. Sacchi Landriani, H. Vandeven. |

Series | ICASE report -- no. 89-42., NASA contractor report -- 181876., NASA contractor report -- NASA CR-181876. |

Contributions | Vandeven, H., Langley Research Center. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL16122128M |

other spectral methods based on other orthogonal polynomials are used to obtain spectral solutions on unbounded intervals ([30], [31]). Spectral collocation methods are e cient and highly accurate techniques for numerical solution of nonlinear dif-ferential equations. The basic idea of the spectral collocation method is to assumeFile Size: KB. The Two- and Three-Dimensional Navier-Stokes Equations [] Background []. The Navier-Stokes equations describe the motion of a fluid. In order to derive the Navier-Stokes equations we assume that a fluid is a continuum (not made of individual particles, but rather a continuous substance) and that mass and momentum are conserved.

CONVERGENCE ANALYSIS OF SPECTRAL COLLOCATION the boundary condition at a singularity and solves the reformulated boundary value problem with a commonly used Gauss–Lobatto collocation scheme. Spectral convergence of the Legendre and method. Moreover,amongthesethreeschemes,onlyMethodCisequivalenttoa. Stokes equation in two and three dimensions by applying curl to the Navier-Stokes equation. The following is a common way of deriving vorticity equa-tion. First note that vorticity is de ned as w= r u, observe the following identity 1 2 r(uu) = (ur)u+ u (r u) Date: Decem Key words and phrases. Fourier Spectral Method, Navier-Stokes File Size: 1MB.

SPECTRAL METHODS IN IRREGULAR DOMAINS 3 then φ(ξ): Ω′ → R is a regularized approximation to χ Ω such that limξ→0 φξ = χΩ. The key idea of the Smoothed boundary method (SBM) is that when ξ → 0 the solutions u(ξ) j of Eqs. () on any domain Ω. 5 Steady Stokes and Navier–Stokes Equations Steady Velocity–Pressure Formulation Stokes Equations The Weak Formulation The Spectral-Element Method Collocation Methods on Single and Staggered Grids Linear Systems, Algorithms, and Preconditioners

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Get this from a library. A multidomain spectral collocation method for the Stokes problem. [G Sacchi Landriani; H Vandeven; Langley Research Center.].

In this paper, we develop a multi-domain spectral collocation method for the Stokes problem. The Stokes equations describe the motion of an incompressible fluid at very low Reynolds num- bers. However, the need to have efficient Stokes solvers is not solely limited to inertia free flows, but is also important when solving the time-dependent Cited by: 4.

M.G. Macaraeg and C.L. Streett, A spectral multi-domain technique with application to generalized curvilinear coordinates, NASA TMLangley, VA (). Hussaini et al. / Spectral collocation methods [38] A. Majda, J. McDonough and S. Osher, The Fourier method for nonsmooth initial data, Math. Comp.

32 () Cited by: The Stokes equations are solved using spectral methods with staggered and nonstaggered grids. Numerous ways to avoid the problem of spurious pressure modes are presented, including new techniques using the pseudospectrdJ method and a method solving the weak.

Sacchi-Landriani, G., Vandeven, H. (): A multidomain spectral collocation method for the Stokes problem. ICASE Reportsubmitted to Google ScholarCited by: 1. () A multidomain spectral collocation method for the Stokes problem. Numerische Mathematik() Truncation versus mapping in the spectral approximation to Cited by: The method is a multidomain bivariate spectral local linearisation method (MD-BSLLM), Legendre-Gauss-Lobatto grid points, a local linearisation technique, and the spectral collocation method to.

This paper gives a description of multidomain solution of advection problems. Multidomain solution requires interface conditions, and such conditions are constructed on the basis of open (or transparent) boundary conditions.

The potential for parallel computations is one of the motivations behind multidomain techniques, and we will deal with this, specifically directed towards distributed Cited by: 5.

The authors present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems.

A model Stokes problem is studied in detail, and. SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () Polynomial collocation using a domain decomposition solution to parabolic PDE's via the penalty method and explicit/implicit time by: simulation is performed by using the projection method combined with a Chebyshev collocation spectral method.

The incompressible Navier-Stokes equations are formulated in terms of the primitive variables, velocity and pressure.

The time integration of the spectrally discretized, incompressible Navier-Stokes equations is performed by a second. () Chebyshev spectral collocation method approximations of the Stokes eigenvalue problem based on penalty techniques. Applied Numerical Mathematics() Numerical scattering for the defocusing Davey–Stewartson II equation for initial data with compact by: This paper has a dual purpose: it presents a multidomain Chebyshev method for the solu.

tion of the two-dirnensional reactive compressible Navier-Stokes equations, and it reports the results of the application of this (:()de to tile numerical simulations of high Math number reaet;ive flows in recessed by: A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids.

The method is easy to implement since it involves one-dimensional operations only, and does not involve surface or volume integrals. Universal reconstructions are ob.

Modern strategies for constructing spectral approximations in complex domains, such as spectral elements, mortar elements, and discontinuous Galerkin methods, as well as patching collocation, are introduced, analyzed, and demonstrated by means of numerous numerical examples.

Representative simulations from continuum mechanics are also shown. Some recent developments stressed in the book are iterative techniques (including the spectral multigrid method), spectral shock-fitting algorithms, and spectral multidomain methods.

The book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance.

Spectral methods have been proposed to solve fractional di erential equa-tions, such as the Legendre collocation method [20, 36], Legendre wavelets method [32, 34], homotopy perturbation method [40] and Jacobi-Gauss-Lobatto collocation method [4].

The authors in [12, 13, 39] constructed an e cient spec-File Size: KB. A Variational Spectral Method 3 velocity. Other treatments of spectral approximation techniques such as spectral tau method and collocation method for the problem (), see for example, [14,15] and the references therein.

Our method is as following. First, we apply. tion formula, complex singularities, Chebyshev–Pad´e approximation, blow-up problem, the Burgers equation AMS subject classiﬁcations. 65M70, 65M50, 41A20, 41A21 DOI.

/ 1. Introduction. The Chebyshev spectral method (the phrase spectral method is synonymous with spectral collocation method in this article) is a method for the. A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.

In this notebook the spectral collocation method is used to find the eigenvalues of the Orr-Sommerfeld equation for the linear stability of plane Poiseuille Flow. Spectral Collocation Method Applied to Nonlinear Boundary Value Problem: In this notebook the spectral collocation method is used to solve a nonlinear boundary value problem that has.arXivv1 [] 27 Jan Hermite spectral collocation methods for fractional PDEs in unbounded domains Tao Tang1,∗, Huifang Yuan2, and Tao Zhou3 1 Departmentof Mathematics,Southern Universityof Sciences andTechnology,Shen- zhen, China.

2 Department of Mathematics, Hong Kong Baptist University, Hong Kong, China. 3LSEC, Institute of Computational File Size: KB. Liu, Vinokur, Wang - Spectral difference method for unstructured grids I:Basic formulation, JCP () pp and Sun, Wang, Liu - High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids, Commun.

Comput. Phys., Vol. 2, No. 2, pp. P.S.