A multidomain spectral collocation method for the Stokes problem by G. Sacchi Landriani

Cover of: A multidomain spectral collocation method for the Stokes problem | G. Sacchi Landriani

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

Written in English

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StatementG. Sacchi Landriani, H. Vandeven.
SeriesICASE report -- no. 89-42., NASA contractor report -- 181876., NASA contractor report -- NASA CR-181876.
ContributionsVandeven, H., Langley Research Center.
The Physical Object
Pagination1 v.
ID Numbers
Open LibraryOL17631947M

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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 A multidomain spectral collocation method for the Stokes problem book, 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. A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems N. Mai-Duy∗ and R.I. Tanner School of Aerospace, Mechanical and Mechatronic Engineering The University of Sydney, NSWAustralia Submitted to Journal of Computational and Applied Mathematics,9thCited by: We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs).

An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable by: 8.

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 A well-posed optimal spectral element approximation for the Stokes problem (SuDoc NAS ) [Maday, Y.] on *FREE* shipping on qualifying offers.

A well-posed optimal spectral element approximation for the Stokes problem (SuDoc NAS )Author: Y. Maday. A Spectral FC Solver for the Compressible Navier-Stokes Equations in General Domains I: Explicit time-stepping Nathan Albin and Oscar P.

Bruno Ap Abstract We present a Fourier Continuation (FC) algorithm for the solution of the fully nonlinear compressible Navier-Stokes equations in general spatial domains. The new scheme is based on.

We also discuss interface conditions for the two dimensional problem and the switching procedure between WENO and spectral subdomains.

The Hybrid method is ap-plied to the two-dimensional Shock-Vortex Interaction and the Richtmyer-MeshkovInstability (RMI) problems. Key words: Spectral, WENO, Multi-resolution, Multi-Domain, Hybrid, Conservation Laws.

The Stokes problem in a tridimensional axisymmetric domain results into a countable family of two-dimensional problems when using the Fourier coe -cients with respect to the angular variable. Relying on this dimension reduction, we propose and study a mortar spectral element discretization of the problem.

A free boundary problem; An example in an unbounded domain; The nonlinear Schroedinger equation; Zeroes of Bessel functions; An example in two dimensions. Poisson’s equation; Approximation by the collocation method; Hints for the implementation; The incompressible Navier-Stokes equations.

Spectral Elements for Transport-Dominated Equations. The numerical dissipation operating in a specific spectral multidomain method model developed for the simulation of incompressible high Reynolds number turbulence in doubly periodic domains is investigated. The method employs Fourier discretization in the horizontal directions and the discretization in the vertical direction is based on a Cited by: Fast Algorithms for Spectral Collocation with Non-Periodic Boundary Conditions W.

Lyons a,1, H. Ceniceros 2, S. Chandrasekaranb and M. Guc aDepartment of Mathematics, University of California, Santa Barbara, CAUSA bDepartment of Electrical and Computer Engineering, University of California, Santa Barbara, CAUSA cDepartment of Mathematics, University of California Cited by: 7.

Ashrafi, M.Y M. Alineia et al:Spectral Collocation Method for the Numerical Solution of the Gardner and Huxley Equations 73 and using (7), the coefficients aj are defined as a j= 2 N ∑N n=0 ′′ T⋆(x n)u(xn,t).

(9) The first three derivatives of approximate solution u at the Chebyshev-Gauss-Lobatto points in the interval [a,b] xn. parameter and present some numerical experiments concerning the penalty spectral element method.

The continuous, penalized and discrete problems Let Ω be a bounded connected open set in Rd, d = 2 or 3, with a Lipschitz-continuous boundary ∂Ω.

The Stokes problem in this domain reads ⎧ ⎨ ⎩ −νΔu+gradp = f in Ω, divu =0 in Ω, u Cited by: 3. A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems N. Mai-Duy∗, R.I. Tanner School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSWAustralia Received 9 September ; received in revised form 28 January Abstract.Local Boundary Condition Based Spectral Collocation Methods for 2D and 3D Navier-Stokes Equations Hans Johnston UMass Amherst Cheng Wang UMass Dartmouth Jian-Guo Liu Duke U.

Charlie Doering U. Michigan Wednesday, Septem   We consider a new least‐squares spectral collocation scheme for the Stokes and the Navier‐Stokes equations. By introducing the Clenshaw‐Curtis quadrature rule for imposing the average pressure to be zero we reduce the condition numbers of the over‐determined systems.

All computations are performed with an explicit scheme and saves a lot of CPU time compared to implicit by: 3.

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