3 edition of **Accuracy of least-squares method for the Navier-Stokes equations** found in the catalog.

Accuracy of least-squares method for the Navier-Stokes equations

Pavel B. Bochev

- 328 Want to read
- 23 Currently reading

Published
**1993** by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, DC], [Springfield, Va .

Written in English

- Least squares.,
- Finite element method.

**Edition Notes**

Other titles | Accuracy of least squares methods for .... |

Statement | Pavel B. Bochev and Max D. Gunzburger. |

Series | NASA technical memorandum -- 106209., ICOMP -- no. 93-19., ICOMP -- no. 93-19. |

Contributions | Gunzburger, Max D., United States. National Aeronautics and Space Administration. |

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

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15387396M |

Research Interests. My research is mainly focused on development and analysis of efficient and structure-preserving numerical methods for kinetic equations (a mesoscopic description of many-particle systems with the nonlinear Boltzmann equation as a prominent example) and related problems arising in multiscale modeling and simulation. Sep 15, · 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 tropheesrotary-d1760.com by: 3. A catalogue record for this book is available from the British Library techniques 59 The SUPG method 60 The Galerkin/Least-squares method 63 The stabilization parameter Strain rate and spin tensors The stress tensor in a Newtonian fluid The Navier—Stokes . In this work a higher-order (>2) accurate finite volume method for the resolution of the Euler/Navier–Stokes equations on Chimera grids is presented. The formulation is based on the use of Moving Least Squares (MLS) approximations for transmission of Author: Luis Ramírez, Xesús Nogueira, Pablo Ouro, Fermín Navarrina, Sofiane Khelladi, Ignasi Colominas.

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow tropheesrotary-d1760.com: George C. Bourantas, Benjamin F. Zwick, Grand R. Joldes, Vassilios C. Loukopoulos, Angus C. R. Tavne.

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Cambridge Univ. Press, Cambridge (in press). Chang, Least squares finite-element method for incompressible flow in 3-D Accuracy of least-squares method for the Navier-Stokes equations book. Chang, Piecewise linear approach to the Stokes equations in 3-D (in press).

Accuracy of least-squares methods for the Navier-Stokes equations 7. tropheesrotary-d1760.com by: ACCURACY OF LEAST-SQUARES METHODS FOR THE NAVIER-STOKES EQUATIONS* Pavel B. Bochev Virginia Polytechnic Institute and State University Blaeksburg, Virginia and Max D.

Gunzburger Institute for Computational Mechanics in Propulsion Lewis Research Center Cleveland, Ohio and Virginia Polytechnic Institute and State University.

Get this from a library. Accuracy of least-squares method for the Navier-Stokes equations. [Pavel B Bochev; Max D Gunzburger; United States. National Aeronautics and Space Administration.].

A LEAST-SQUARES FINITE ELEMENT METHOD FOR INCOMPRESSIBLE NAVIER-STOKES PROBLEMS Bo-nan Jiang* Institute for Computational Mechanics in Propulsion Lewis Research Center Cleveland, Ohio SUMMARY A least-squares finite element method, based on the velocity-pressure-vorticity for. ANALYSIS OF LEAST-SQUARES FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS ∗ PAVEL B.

BOCHEV † Abstract. In this paper we study ﬁnite Accuracy of least-squares method for the Navier-Stokes equations book methods of least-squares type for the stationary, incompressible Navier-Stokes equations in 2 and 3 dimensions. We consider methods based on. A spectral collocation approximation of first-order system least squares for incompressible Stokes equations was analyzed in Kim et al.

(), and finite element approximations for incompressible Navier–Stokes equations were developed in Bochev et al. (,).The aim of this paper is to analyze the first-order system least-squares pseudo-spectral method for incompressible Navier Cited by: The time-dependent Navier–Stokes equations and the energy balance equation for an incompressible, constant property fluid in the Boussinesq approximation are solved by a least-squares finite.

As a consequence of this estimate, we will provide a convergence analysis for the linearization process on solving Navier—Stokes equations, which uses the div least-squares method for solving. Least-squares finite element methods have become increasingly popular for the approximate solution of first-order systems of partial differential equations.

Here, after a brief review of some existing theories, a number of issues connected with the use of such methods for the velocity-vorticity-pressure formulation of the Stokes equations in two dimensions in realistic settings are studied Cited by: Oct 21, · An approach for the creation of high-accuracy versions of the collocations and least squares method for the numerical solution of the Navier-Stokes equations is Cited by: The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution.

A LEAST-SQUARES FINITE ELEMENT METHOD FOR THE NAVIER-STOKES EQUATIONS PAVEL B. BOCHEV AND MAX D. GUNZBURGER an extensive numerical study of the accuracy of the least-squares finite element method applied to (l)-(6) and h ave found that, at the least, approximations are nearly optimally accurate in the.

The least-squares finite element method (LSFEM), which is based on minimizing the l 2-norm of the residual, has many attractive advantages over Galerkin finite element method (GFEM).It is now well established as a proper approach to deal with the convection dominated fluid dynamic tropheesrotary-d1760.com: Rajeev Kumar, Brian H.

Dennis. Book and papers. Bochev and M. Gunzburger; Least Squares Finite Element Methods, A least-squares finite element method for the Navier-Stokes equations, Appl. Math. Lett. 6P. Bochev and M. Gunzburger; The accuracy of least-squares methods for the Navier-Stokes equations, Comput.

Fluids 22of Philosophy and entitled A Least-Squares Finite Element Method for the Stokes and Navier-Stokes Equations. Month and Year of Submission: December In this thesis the least-squares ﬁnite element method for ﬁrst-order systems is set out.

We present a number of established ﬁrst-order reformulations of the planar Stokes equations. A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids.

The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes.

LEAST SQUARES PRECONDITIONERS FOR STABILIZED DISCRETIZATIONS OF THE NAVIER-STOKES EQUATIONS ⁄ HOWARD ELMANy, VICTORIA E.

HOWLEz, JOHN SHADIDx, DAVID SILVESTER{, AND RAY TUMINAROk Abstract. This paper introduces two stabilization schemes for the Least Squares Commutator. Kumar, Rajeev, and Dennis, Brian H. "A Least-Squares Galerkin Split Finite Element Method for Compressible Navier-Stokes Equations." Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering tropheesrotary-d1760.com by: 1.

This paper studies a new alteration of Yosida algebraic splitting methods for the Navier--Stokes equations. By applying the usual or pressure-corrected Yosida splitting techniques to discretizations written in terms of velocity and pressure updates $(u^{n+1}-u^n,p^{n+1}-p^n)$, we show that the accuracy is increased by one full order in $\Delta t$ without any additional cost in the respective Cited by: 8.

Accuracy of least-squares methods for the Navier-Stokes equations, (with M. Gunzburger) NASA Technical Memorandum,ICOMP, June On quadratic invariants and simplectic structure, (with C. Scovel) LA-UR, Los Alamos National Laboratory, Finite Element Methods: a variational approach to theory and practice, Sandia National Laboratories, Report.

Abstract. The method of collocations and least squares, which was previously proposed for the numerical solution of the two-dimensional Navier–Stokes equations governing steady incompressible viscous flows, is extended here for the three-dimensional tropheesrotary-d1760.com by: 9. L.P. Franca et al./ Stabilized Finite Element Methods 3 STABILIZED FINITE ELEMENT METHODS The standard Galerkin method is constructed based on the variational formula-tion (3) by taking a subspace of H1 0 (Ω) spanned by continuous piecewise polynomials.

In two dimensions the support of these functions is a mesh partition of Ω into tri-Cited by: in the model. Using these auxiliary variables, different alternative Least-Squares finite element models are developed and investigated. In this research, the vorticity and stress based alternative Least-Squares finite element formulations of Navier-Stokes equations are developed and are verified with the.

Least squares finite element method with high continuity NURBS basis for incompressible Navier-Stokes equations. Authors: De-Xiang Chen: State Key Lab for Strength and Vibration of Mechanical Structures, Xian Jiaotong University, XianChina:Cited by: 2.

The time-discontinuous Galerkin least-squares nite element discretization results in a large system of nonlinear algebraic equations. For unsteady problems, a linear-in-time approximation of the space-time Galerkin least-squares variational equation is needed.

In this thesis we propose a new method to solve the nonlinear algebraic. The traditional pressure-correction methods are widely used to solve N-S equations. An example of this approach is the SIMPLE algorithm [27].

This method integrates the Navier-Stokes equations in time at each time-step by firstly solving the momentum equations using an approximate pressure field to yield an intermediate velocity field that will not, in general, satisfy tropheesrotary-d1760.com: Dan Sun, Yanting Ai, Wanfu Zhang, Jiangang Yang.

The method of manufactured solutions is used to verify the order of accuracy of two fi-nite-volume Euler and Navier-Stokes codes.

The Premo code employs a node-centered ap-proach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe’s upw ind method with MUSCL extrapolation for the. A LOW-RANK SOLVER FOR THE NAVIER{STOKES EQUATIONS WITH UNCERTAIN VISCOSITY KOOKJIN LEEy, HOWARD C.

ELMANz, AND BEDRICH SOUSED IKx Abstract. We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier{Stokes equations with uncertain viscosity. The method is based on lineariza. LEAST SQUARES PRECONDITIONERS FOR STABILIZED DISCRETIZATIONS OF THE NAVIER-STOKES EQUATIONS The other method is derivedbytreating\highfrequency"and\lowfrequency"componentsofthepressure space separately in a manner reminiscent of the development of multigrid methods.

In (Tiwari et al. ), this method has been applied to a grid free framework with the help of the weighted least squares method. The scheme gives accurate results for the incompressible Navier–Stokes equations. The occurring Poisson equation for the pressure field is solved by a grid free method. – Developed a novel ﬁnite element method called least-squares/Galerkin split ﬁnite element method to solve Navier-Stokes equations.

This method treats the ﬁrst-order terms with the least-squares method and the second-order terms with Galerkin method; thereby keeps the advantages and avoids the drawbacks of the two.

This paper presents a p‐ version least squares finite element formulation (LSFEF) for two‐dimensional, incompressible, non‐Newtonian fluid flow under isothermal and non‐isothermal conditions.

The dimensionless forms of the diffential equations describing the fluid motion and heat transfer are cast into a set of first‐order. Jian Li, Zhangxin Chen, Optimal L 2, H 1 L ∞ analysis of finite volume methods for the stationary NavierStokes equations with large data, Numerische Mathematik, v n.1, p, January Cited by: Dec 01, · A Finite Element Based Level-Set Method for Multiphase Flows (B Engquist & A-K Tornberg) The GHOST Fluid Method for Viscous Flows (R P Fedkiw & X-D Liu) Factorizable Schemes for the Equations of Fluid Flow (D Sidilkover) Evolution Galerkin Methods as.

Preface This is a set of lecture notes on ﬁnite elements for the solution of partial differential equations. The approach taken is mathematical in nature with a strong focus on the.

With the advent of super computers during the last ten years, the numerical simulation of viscous fluid flows modeled by the Navier-Stokes equations is becoming a most useful tool in Aircraft and Engine Design.

In fact, compressible Navier-Stokes solvers tend to constitute the basic tools for many. The method was devised to compute the eigenvalues of the 2D MHD system in [ AIAA paper]. Consistent LSQ Norm of the 2D Euler Equations:[ pdf] A dimensionally-consistent discrete least-squares norm for the 2D Euler equations is derived.

It can be used to solve the Euler equations by the discrete least-squares method. Apr 01, · The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared tropheesrotary-d1760.com by: 4.

Application to the Numerical Simulation of Compressible Viscous Flows --Solution of the Compressible Navier-Stokes Equations by Least-Squares and Finite Element Methods order to compare accuracy and efficiency of Navier-Stokes solvers on selected external and internal flow problems using different numerical approaches.

Multigrid Method. High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of Author: M.

Deville, P. Fischer, E. Mund. Effect of grid quality on the accuracy and convergency of computations. Susumu Shirayama and; A Data-Parallel Line Relaxation method for the Navier-Stokes equations. Michael Wright, Graham Candler, Deepak Bose, Michael Wright, An adaptive least-squares method for the compressible Euler equations.

F. Taghaddosi, W. Habashi, G. Guevremont.The linearized Navier-Stokes equations represent a linearization to the full set of governing equations for a compressible, viscous, and nonisothermal flow (the Navier-Stokes equations).

It is performed as a first-order perturbation around the steady-state background flow defined by its pressure, velocity, temperature, and density (p 0, u 0.P. Bochev and M. Gunzburger; A least-squares finite element method for the Navier-Stokes equations, Appl. Math. Lett. 6P.

Bochev and M. Gunzburger; The accuracy of least-squares methods for the Navier-Stokes equations, Comput. Fluids 22