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2 edition of Runge-Kutta discontinuous Galerkin method for convection-dominated problems found in the catalog.

Runge-Kutta discontinuous Galerkin method for convection-dominated problems

B. Cockburn

Runge-Kutta discontinuous Galerkin method for convection-dominated problems

by B. Cockburn

  • 231 Want to read
  • 12 Currently reading

Published by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va .
Written in English

    Subjects:
  • Algorithms.,
  • Conservation laws (Mathematics),
  • Differential equations.,
  • Exponential functions.,
  • Galerkin methods.,
  • Nonlinear systems.,
  • Runge-Kutta formulas.

  • Edition Notes

    Other titlesRunge Kutta discontinuous Galerkin method for convection dominated problems, ICASE
    StatementBernardo Cockburn, Chi-Wang Shu.
    SeriesICASE report -- no. 2000-46, NASA/CR -- 2000-210624, NASA contractor report -- NASA CR-2000-210624.
    ContributionsShu, Chi-Wang., Institute for Computer Applications in Science and Engineering., Langley Research Center.
    The Physical Object
    Pagination75 p. :
    Number of Pages75
    ID Numbers
    Open LibraryOL19394554M

    These methods are an extension of the Runge{Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-di usion sys-tems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated problems. It is proven that for scalarFile Size: KB. as follows. First we discretize () in space using the Discontinuous Galerkin Method. The resulting equation can be put in ODE form as j¡uh-Lh(uh, yh(t)) Then, this ODE is discretized in time using the TVD Runge-Kutta time discretization .

    limiter and can be applied to Runge-Kutta discontinuous Galerkin (RKDG) method and weighted essentially non-oscillatory (WENO) finite volume schemes of arbitrary order of accuracy on arbi-trary meshes to ensure the positivity-preserving property without affecting the originally designed high order accuracy [33, 34, 35].Cited by: 7. Downloadable! Discontinuous Galerkin (DG) method is a popular high-order accurate method for solving unsteady convection-dominated problems. After spatially discretizing the problem with the DG method, a time integration scheme is necessary for evolving the result. Owing to the stability-based restriction, the time step for an explicit scheme is limited by the smallest .

      Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations - Volume 17 Issue 2 - X. Liang, A. Q. M. Khaliq, Y. XingCited by:   We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [9, 8, 7, 6] for solving conservation Laws with increased CFL new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG by: 8.


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Runge-Kutta discontinuous Galerkin method for convection-dominated problems by B. Cockburn Download PDF EPUB FB2

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of by: In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems.

These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems.

These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of by: 4. 1 Motivation. The discontinuous Galerkin (DG) method is a robust and compact finite element projection method that provides a practical framework for the development of high-order accurate methods using unstructured grids.

The method is well suited for large-scale time-dependent computations in which high accuracy is required. Double Mach reflection problem.

This model problem is originally solve the two-dimensional Euler equations in a computational domain of [0, 4] × [0, 1].The reflection boundary condition is used at the wall, which for the rest of the bottom boundary (the part from x = 0 to x = 1 6), the exact post-shock condition is the top boundary is the exact motion of the Author: Jun Zhu, Jianxian Qiu, Chi-Wang Shu.

Abstract. In these notes, we study the Runge Kutta Discontinuous Galerkin method for numericaly solving nonlinear hyperbolic systems and its extension for convection-dominated problems, the so-called Local Discontinuous Galerkin method.

Examples of problems to which these methods can be applied are the Euler equations of gas dynamics, Cited by: The Runge-Kutta discontinuous Galerkin method (RKDG method) is widely used nowadays. The RKDG method is characterized by a high-order accurate solution.

These methods are an extension of the Runge--Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, high-order formal accuracy, and easy handling of complicated geometries for convection-dominated by: For the choice Vh DV0 h and quadrature rules over the edges exact for constants, the resulting scheme is nothing but a finite volume, monotone scheme in the scalar case.

Thus, the discretization by the discontinuous Galerkin method can be considered as a high-order accurate extension of finite volume, monotone schemes. Liu and L.-Z. Fang, A WENO algorithm for the growth of ionized regions at the reionization epoch, New Astronomy, v13 (), pp L.

Yuan and C.-W. Shu, Discontinuous Galerkin method for a class of elliptic multi-scale problems, International Journal for Numerical Methods in Fluids, v56 (), pp The Finite Element Method for Elliptic Problems Amsterdam-New York: North-Holland, C W.

Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. A Fully-Discrete Local Discontinuous Galerkin Method for. The Runge--Kutta discontinuous Galerkin (RKDG) method is a high order finite element method for solving hyperbolic conservation laws. It uses ideas from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, total variation diminishing (TVD) Runge--Kutta time discretizations, and by: In the DG method, the approximate solution is discontinuous only in time, not in space; in fact, the space discretization is the standard Galerkin discretization with continu- ous finite elements.

This is in strong contrast with the space discretizations. DISCONTINUOUS GALERKIN METHOD Hyperbolic equations Setup of the Runge-Kutta DG schemes We are interested in solving a hyperbolic conservation law ut + f(u)x = 0 In 2D it is ut + f(u)x +g(u)y = 0 and in system cases u is a vector, and.

THE RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR CONSERVATION LAWS IV: THE MULTIDIMENSIONAL CASE BERNARDO COCKBURN, SUCHUNG HOU, AND CHI-WANG SHU ABSTRACT.

In this paper we study the two-dimensional version of the Runge- Kutta Local Projection Discontinuous Galerkin (RKDG) methods File Size: KB.

the Runge-Kutta Discontinuous Galerkin (RKDG) method for systems of hyperbolic conservation laws and convection-dominated problems.

Together with the ENO and WENO schemes, the RKDG method is one of the most powerful and widely used high-order accurate methods for compressible ows. It combines the advantages of a shock-capturing. $\begingroup$ Convection-dominated equation normally have strongly irregular solutions (large jumps, discontinuities), traditional numerical methods always assume the solution is smooth.

That's why many people using Discontinuous Galerkin finite element to numerically solve this type of problems. $\endgroup$ – Shuhao Cao Jun 18 '13 at Cockburn, Bernardo; Shu, Chi-Wang. The Runge-Kutta Local Projection P1-Discontinuous-Galerkin Finite Element Method for Scalar Conservation by: Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods.

Building Bridges: Connections and Challenges in Modern Approaches to Cited by: Discontinuous Galerkin (DG) methods are a class of finite-element methods us- For hyperbolic problems or convection-dominated problems such as Navier- then explicit time marching methods such as the Runge-Kutta methods described above suffer from severe time-step restrictions.

It is an important and. Get this from a library! Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. [B Cockburn; Chi-Wang Shu; Institute for Computer Applications in .55 References! B. Cockburn and C.-W.

Shu: Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems, J. Sci. Comput., 16 (), ! Y. Xu and C.-W. Shu: Local Discontinuous Galerkin Methods for High- Order Time-Dependent Partial Differential Equations,   The Runge-Kutta discontinuous Galerkin (RKDG) methods are efficient methods for solving nonlinear conservation laws, which are high-order accurate and highly parallelizable, and can be easily used to handle complicated geometries and boundary conditions.

C.-W., Runge-Kutta discontinuous Galerkin methods for convection-dominated problems Cited by: 5.