# Weighted essentially non-oscillatory schemes on triangular meshes

- 1998
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Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor , Hampton, VA, Springfield, VA

Unstructured grids (Mathematics), Finite volume method, Triangles, Computational

Statement | Chang-Qing Hu and Chi-Wang Shi. |

Series | ICASE report -- no. 98-32., [NASA contractor report] -- NASA/CR-1998-208459., NASA contractor report -- NASA CR-208459. |

Contributions | Shi, Chi-Wang., Institute for Computer Applications in Science and Engineering. |

The Physical Object | |
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Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL17581937M |

OCLC/WorldCa | 41359270 |

WENO SCHEMES ON TRIANGULAR MESHES Positivity of Linear Weights for the Fourth-Order Scheme From Sectionthere is a degree of freedom (which was chosen to be °1)inthe determinationofthelinearweights°s in().Ourobjectiveistousethisdegreeoffreedom to obtain non-negative linear weights.

Weighted essentially non-oscillatory schemes on triangular meshes (ICASE report) Unknown Binding – January 1, by Chang-Qing Hu (Author)Author: Chang-Qing Hu. Abstract.

### Details Weighted essentially non-oscillatory schemes on triangular meshes EPUB

In this paper we construct high-order weighted essentially non-oscillatory schemes on two-dimensional unstructured meshes (triangles) in the finite volume formulation.

We present third-order schemes using a combination of linear polynomials and fourth-order schemes using a combination of quadratic by: In this paper, we review and construct fifth- and ninth-order central weighted essentially nonoscillatory (WENO) schemes based on a finite volume formulation, staggered mesh, and continuous extension of Runge–Kutta methods for solving.

Get this from a library. Weighted essentially non-oscillatory schemes on triangular meshes. [Chang-Qing Hu; Chi-Wang Shi; Institute for Computer Applications in Science and Engineering.].

Chen Hu, Chi-Wang Shu In this paper we construct high-order weighted essentially non-oscillatory schemes on two-dimensional unstructured meshes (triangles) in the finite volume formulation.

### Description Weighted essentially non-oscillatory schemes on triangular meshes PDF

We present third-order schemes using a combination of linear polynomials and fourth-order schemes using a combination of quadratic polynomials. In this paper, we design a new type of high order finite volume weighted essentially nonoscillatory (WENO) schemes to solve hyperbolic conservation laws on triangular meshes.

The main advantages of these schemes are their compactness and robustness and that they could maintain a good convergence property for some steady state by: 9. Abstract In this paper, we design a new type of high order finite volume weighted essentially nonoscillatory (WENO) schemes to solve hyperbolic conservation laws on triangular meshes.

The main. INTRODUCTION In this paper, the weighted essential non-oscillatory (WENO) schemes are used to simulate the tidal bore of the two-dimensional shallow water equations for. on two dimensional triangular meshes. Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes are high order numerical methods for solving ().

ENO schemes were designed by Harten et. In this paper we construct high order weighted essentially non-oscillatory (WENO) schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. We present third order schemes using a combination of linear polynomials, and fourth order schemes using a combination of quadratic polynomials.

### Download Weighted essentially non-oscillatory schemes on triangular meshes FB2

Thispaperproposesanewadaptive nonlinear ADER scheme on unstruc- tured triangular meshes for solving Cauchy problems for scalar conservation laws of the form ∂u ∂t +∇f(u)=0, (1) where for some bounded open domain Ω⊂ R2, and time interval I =[0,T], T>0, the function u: I×Ω → R is the unknown solution of (1), and where f(u)=(f 1(u),f 2(u))T denotes the ﬂux tensor.

ADER Schemes on Adaptive Triangular Meshes for Scalar Conservation Laws Martin K¨aser and Armin Iske weighted essentially non-oscillatory (WENO) reconstruction schemes. of this paper can be viewed as an extension of previous ADER schemes to adaptive triangular meshes.

The outline of this paper is as follows. In the following Section 2, the. In this paper we design a new third order finite volume weighted essentially non-oscillatory (WENO) to solve three dimensional hyperbolic conservation laws () {u t + f (u) x + g (u) y + r (u) z = 0, u (x, y, z, 0) = u 0 (x, y, z), on tetrahedral by: Abstract In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) lim- iter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional un- structured triangular meshes, to the correction procedure via reconstruction (CPR) framework for solving nonlinear hyperbolic conservation laws on two-dimensional un- structured triangular meshes.

In this paper, we investigate a simple limiter using weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, Author: ZhongXinghui, ShuChi-Wang.

Key words. 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]. This paper has been cited at least times by early 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: In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for the hyperbolic conservation laws on unstructured quadrilateral and triangular meshes.

As a starting point, a general stencil is selected for the cell with any local topology, and a unified linear scheme can be constructed. Abstract In this paper, we continue our work in [40] and propose a new type of high-order ﬁnite volume multi-resolution weighted essentially non-oscillatory (WENO) schemes to solve hy- perbolic conservation laws on triangular meshes.

In this paper we construct high order Weighted Essentially Non-Oscillatory (WENO) schemes on two dimensional unstructured meshes (triangles) in. 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.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] to three dimensions, and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes.

We use the Lax-Friedrichs. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws by Chi-wang Shu, 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.

We extend the weighted essentially non-oscillatory (WENO) schemes on two dimensional triangular meshes developed in [7] to three dimensions, and con-struct a third order ﬁnite volume WENO scheme on three dimensional tetrahedral meshes.

We use the Lax-Friedrichs monotone ﬂux as building blocks, third order re. Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics Andrew J. Christlieba, James A. Rossmanithb,1, Qi Tangc aDepartment of Mathematics and Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MIUSAAuthor: Qi Tang, Andrew Christlieb, Yaman Guclu, James Rossmanith.

NON-OSCILLATORY SCHEMES FOR HYPERBOLIC CONSERVATION LAWS CHI-WANG SHU * Abstract. In these lecture notes we describe the construction, analysis, and application of ENO (Es-sentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic con- not decay in magnitude when the mesh is refined.

It is a nuisance. Balsara, D., and Shu, C.-W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of by: In this paper, a third-order weighted essentially non-oscillatory (WENO) scheme is developed for the hyperbolic conservation laws on unstructured quadrilateral and triangular meshes.

As a starting point, a general stencil is selected for the cell with any local topology, and a unified linear scheme can be constructed.

However, in the traditional WENO scheme on unstructured meshes. Hu and C.-W. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, Journal of Computational Physics, v (), pp C.

Hu and C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton-Jacobi equations, SIAM Journal on Scientific Computing, v21 (), pp. On essentially non-oscillatory schemes on unstructured meshes [microform]: analysis and implementation / R. Abgrall Institute for Computer Applications in Science and Engineering, NASA Langley Research Center ; National Technical Information Service, distributor Hampton, VA: [Springfield, Va In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes.Cartesian meshes regardless of the domain boundary shape.

This method is expected to very useful in a wide range of applications involving level set methods and front propagation. In [1], we have developed high order essentially non-oscillatory (ENO) Lagrangian schemes based on the Lax-Wendroﬀ (LW) type time discretization procedure.

Exten.