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3 edition of High order essentially non-oscillatory schemes for Hamilton-Jacobi equations found in the catalog.

High order essentially non-oscillatory schemes for Hamilton-Jacobi equations

Stanley Osher

High order essentially non-oscillatory schemes for Hamilton-Jacobi equations

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  • 25 Currently reading

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

    Subjects:
  • Approximation.,
  • Hamilton-Jacobi equation.,
  • Hyperbolic differential equations.

  • Edition Notes

    StatementStanley Osher, Chi-Wang Shu.
    SeriesICASE report -- no. 90-13., NASA contractor report -- 181995., NASA contractor report -- NASA CR-181995.
    ContributionsShu, Chi-Wang., Langley Research Center.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17726221M

    High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations schemes that were introduced in [20, 21], and were based on an Essentially Non-Oscillatory (ENO) reconstruction step [7] that was evolved in time with core ingredient in the derivation of our schemes is a high-order CWENO reconstructions in space. A WENO finite-difference scheme for a new class of Hamilton–Jacobi equations in nonlinear solid mechanics. Victor Lefevre, Alvaro Garnica, Oscar Lopez-Pamies * * Corresponding author for this work. Mechanical Engineering; Research output: Contribution to journal › Article. 3 Scopus by: 2. the Hamilton-Jacobi framework. This Hamilton-Jacobi WENO or HJ WENO scheme turns out to be very useful for solving equation 1 as it reduces the errors by more than an order of magnitude over the third order accurate HJ ENO scheme for typical applications. The HJ WENO approximation of (φ− x) i is a convex combination of the ap-.   The high order moving mesh arbitrary Lagrangian Eulerian (ALE) weighted essentially non-oscillatory (WENO) finite difference scheme, recently developed in, is a good choice and will be used in this paper. In two dimensions, this method is based on moving quadrilateral meshes, which are often used in Lagrangian type methods.


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High order essentially non-oscillatory schemes for Hamilton-Jacobi equations by Stanley Osher Download PDF EPUB FB2

High Order Essentially Non-Oscillatory Schemes for Hamilton-Jacobi Equations [Stanley Osher] on *FREE* shipping on qualifying offers.

In this paper high-order essentially nonoscillatory (ENO) schemes for H–J equations are investigated, which yield uniform high-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives.

The ENO scheme construction procedure is adapted from Cited by: () A Sixth-Order Weighted Essentially Non-oscillatory Schemes Based on Exponential Polynomials for Hamilton–Jacobi Equations. Journal of Scientific Computing() High-order filtered schemes for first order time dependent linear and non-linear partial differential by: High order essentially non-oscillatory (ENO) schemes for H-J equations are investigated which yield uniform high order accuracy in smooth regions and resolve discontinuities in the derivatives.

In this paper we investigate high order High order essentially non-oscillatory schemes for Hamilton-Jacobi equations book non- oscillatory (ENO) schemes for H-J equations, which yield uniform high order accuracy in smooth regions and resolve discontinuities in the derivatives sharply.

The ENO scheme construction procedure is adapted from that for hyperbolic conservation laws. {{Citation | title=High order essentially non-oscillatory schemes for Hamilton-Jacobi equations [microform] / Stanley Osher, Chi-Wang Shu | author1=Osher, Stanley | author2=Shu, Chi-Wang | author3=Langley Research Center | year= | publisher=National Aeronautics and Space Administration, Langley Research Center | language=English }}.

In these lecture notes High order essentially non-oscillatory schemes for Hamilton-Jacobi equations book describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations.

ENO and WENO schemes are high order accurate nite di erence schemes designed for problems with piecewise smooth solutions containing. Zhang and Shu [25], Li and Chan [12] further developed high order WENO schemes for solving two dimensional Hamilton-Jacobi High order essentially non-oscillatory schemes for Hamilton-Jacobi equations book by using the nodal based weighted essentially non-oscillatory.

Buy High Order Essentially Non-Oscillatory Schemes for Hamilton-Jacobi Equations by Stanley Osher (ISBN:) from Amazon's Book Store. Everyday low prices and free delivery on eligible : Stanley Osher. In this study, we present a new sixth-order finite difference weighted essentially non-oscillatory (WENO) scheme for solving Hamilton–Jacobi equations.

The proposed scheme recovers the maximal approximation order in smooth regions without High order essentially non-oscillatory schemes for Hamilton-Jacobi equations book of accuracy at critical points.

We incorporate exponential polynomials into the scheme to obtain better approximation near steep gradients without Cited by: 2. Abstract. In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations.

ENO and WENO schemes are high order accurate finite difference schemes designed Cited by: proposed a general framework for the numerical solution of Hamilton-Jacobi equations using successful methods from hyperbolic conservation laws, many high order numer-ical methods such as the essentially non-oscillatory (ENO) method [22], the weighted essentially non-oscillatory (WENO) method [13] and the discontinuous Galerkin (DG)File Size: 53KB.

Hamilton-Jacobi (H-J) equations are frequently encountered in applications, e.g. in control theory and differential games. H-J equations are closely related to. essentially non-oscillatory, conservation laws, high order accuracy Subject classi cation. Applied and Numerical Mathematics 1. Introduction.

ENO (Essentially Non-Oscillatory) schemes started with the classic paper of Harten, Engquist, Osher and Chakravarthy in [38]. Get this from a library. High order essentially non-oscillatory schemes for Hamilton-Jacobi equations.

[S Osher; C -W Shu; Institute for Computer Applications in Science and Engineering.]. ENO and WENO schemes for Hamilton-Jacobi type equations were designed and applied in [59], [60], [50] and [45]. ENO schemes using one-sided Jocobians for field by field decomposition, which improves the robustness for calculations of systems, were discussed in [25].

High order essentially non-oscillatory schemes for Hamilton-Jacobi equations. [S Osher; C -W Shu] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create. High order finite difference Hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes Feng Zheng1, Chi-Wang Shu2 and Jianxian Qiu3 Abstract In this paper, a new type of high order Hermite weighted essentially non-oscillatory (HWENO) methods is proposed to solve the Hamilton-Jacobi (HJ) equations on unstructured meshes.

We use. In this paper, a class of high order numerical schemes is proposed for solving Hamilton–Jacobi (H–J) equations. This work is regarded as an extension of our previous work for nonlinear degenerate parabolic equations, see Christlieb et al.

[14], which relies on a special kernel-based formulation of the solutions and successive by: 4. Key words: Unequal-sized stencil, weighted essentially non-oscillatory scheme, high-order ap-proximation, Hamilton-Jacobi equation, triangular mesh.

1 Introduction In this paper, we designa class of new third-orderand fourth-orderweighted essentially non-oscillatory (WENO) schemes for solving the Hamilton-Jacobi equations ˆ φ t+H(x,y,t,φ,φ File Size: 2MB.

In this paper we present the first fifth-order central scheme for approximating solutions of one-dimensional Hamilton-Jacobi equations.

The main ingredient in this scheme is a central weighted essentially non-oscillatory reconstruction in space. The expected behavior of the scheme is demonstrated in several numerical by: 5.

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing.

We introduce a new high-resolution central scheme for multidimensional Hamilton?Jacobi equations. The scheme retains the simplicity of the non-oscillatory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J. Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, independent of 1/?t.

By letting?t?0 we obtain a new second-order central scheme in the. Abstract: In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D.

The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping by: In this paper, a high order arbitrary Lagrangian-Eulerian (ALE) finite difference weighted essentially non-oscillatory (WENO) method for Hamilton-Jacobi equations is developed.

This method is based on moving quadrilateral meshes, which are often used in Lagrangian type methods. High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations [Steve Bryson, Doron Levy, NASA Technical Reports Server (NTRS)] on *FREE* shipping on qualifying offers.

We present the first fifth order, semi-discrete central upwind method for approximating solutions of multi-dimensional Hamilton-Jacobi by: We develop high order essentially non-oscillatory (ENO) schemes on non-uniform meshes based on generalized binary trees.

The idea is to adopt an appropriate data structure which allows to communicate information easily between unstructured data structure and virtual uniform : C CecilThomas, J OsherStanley, QianJianliang. ICASE Report No. 00)ICASE HIGH ORDER ESSENTIALLY NON-OSCILLATORY SCHEMES FOR HAMILTON-JACOBI EQUATIONS Shi-ang Stnly shrDTIC She ELECTE ChiWang Sh.

3 MAR19 L D0 Contract No. NAS February Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hamptan, Virginia A high-order weighted essentially non-oscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations R Abedian, H Adibi, M Dehghan Computer Physics Communications (8), S.

Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM Journal on Numerical Analysis, v28 (), pp ] C.-W.

Shu, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, Journal of Computational Physics, v (), pp File Size: KB. schemes. Following such principles, Osher et al. [24,25] designed some high-order accu-rate essentially non-oscillatory (ENO) schemes for solving the Hamilton–Jacobi equations.

Lafon and Osher [17] constructed ENO schemes for solving the Hamilton–Jacobi equations on unstructured meshes. Osher and C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM Journal on Numerical Analysis, v28 (), pp C.-W.

Shu, A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, Journal of Computational Physics v (), pp methods.

We adapt high order schemes for time dependent Hamilton-Jacobi equations in [24, 14, 39] to the static H-J equations in a novel way. First-order sweeping schemes are used as building blocks in our high order methods. The high order accuracy in our schemes results from the high order approximations for the partial derivatives because.

scheme is (formally) rth order accurate. See, e.g., [Z]. There are many TVD schemes constructed in the literature (e.g., [2, 3,9, 10, ).

In [lo], TVD schemes of very high spatial order (up to 15th order) were constructed. These schemes can be used for steady state calculations. and Weighted Essentially Non-Oscillatory (WENO) schemes for struc-tured meshes, and WENO schemes and Discontinuous Galerkin (DG) schemes for unstructured meshes.

Introduction and Properties of Hamilton-Jacobi Equations In these lectures we review high order accurate numerical methods for solv-ing time dependent Hamilton-Jacobi equationsFile Size: 2MB.

In numerical solution of differential equations, WENO (weighted essentially non-oscillatory) methods are classes of high-resolution schemes. WENO are used in the numerical solution of hyperbolic partial differential equations. These methods were developed from ENO methods (essentially non-oscillatory).Finite difference: Parabolic, Forward-time central-space.

for Multi-Dimensional Hamilton-Jacobi Equations Steve Bryson Doron Levyy Abstract We present the rst fth-order, semi-discrete central-upwind method for ap-proximating solutions of multi-dimensional Hamilton-Jacobi equations.

Unlike most of the commonly used high-order upwind schemes, our scheme is formulated as a Godunov-type by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations.

ENO and WENO schemes are high order accurate nite di erence schemes. - Buy High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations book online at best prices in India on Read High-Order Semi-Discrete Central-Upwind Schemes for Multi-Dimensional Hamilton-Jacobi Equations book reviews & author details and more at Free delivery on qualified : Steve Bryson.

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations.

ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The focus of the pdf work pdf to develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal mag-netohydrodynamic (MHD) equations in 2D and 3D.

We make use of the basic unstag-gered constrained transport framework developed by Helzel et al. [21], although weAuthor: Qi Tang, Andrew Christlieb, Yaman Guclu, James Rossmanith.This paper puts forth a high-order weighted essentially non-oscillatory (WENO) finite-difference scheme to numerically generate the viscosity solution of a new class of Hamilton–Jacobi (HJ) equations that has recently emerged in nonlinear solid by: 2.High‐order k‐exact WENO finite volume schemes for solving gas dynamic Euler equations ebook unstructured grids Wanai Li.

Corresponding Author. Department of Engineering Mechanics, Tsinghua University, Beijing, China. Wanai Li, Department of Engineering Mechanics, Tsinghua University, BeijingChina.