3 edition of **Uniform high order spectral methods for one and two dimensional Euler equations** found in the catalog.

Uniform high order spectral methods for one and two dimensional Euler equations

- 206 Want to read
- 9 Currently reading

Published
**1991**
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
.

Written in

- Spectral theory (Mathematics),
- Conservation laws (Mathematics)

**Edition Notes**

Statement | Wei Cai, Chi-Wang Shu. |

Series | ICASE report -- no. 91-26., NASA contractor report -- 187535., NASA contractor report -- NASA CR-187535. |

Contributions | Shu, Chi-Wang., Langley Research Center. |

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

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15390807M |

A Chebyshev generalized finite spectral method is proposed for 2-D linear and nonlinear waves. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor Author: Jian-Ping Wang. Spectral methods involve seeking the solution to a differential equation in terms of a series of known, smooth functions. They have recently emerged as a viable alternative to finite difference and finite element methods for the numerical solution of partial differential equations.

W. Cai and C.-W. Shu, Uniform high order spectral methods for one and two dimensional Euler equations, Journal of Computational Physics, v (), pp W. E and C.-W. Shu, Effective equations and the inverse cascade theory for Kolmogorov flows, . Its spectral accuracy has been demonstrated in the case of shocked solutions of the Burgers equation and the system of one-dimensional compressible Euler equations. This method does not restrict its extension to include multidimensions and multiphase flows, and this will be the subject of future by: 8.

Numerical Methods for! One-Dimensional Heat Equations! One-dimensional ﬂow! Two-dimensional ﬂow! ADI consists of ﬁrst treating one row implicitly with backward Euler and then reversing roles and treating the other by backwards Euler.! Peaceman, D., and Rachford, M. (). Buy Implementing Spectral Methods for Partial Differential Equations: It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave propagation. a field that is inevitably intertwined with higher order Cited by:

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Uniform high-order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the essentially non-oscillatory polynomial (ENO) interpolations into the spectral by: Euler gas dynamics equations.

Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essen-tially Non-Oscillatory polynomial (ENO) interpolations into the spectral methods.

Based on the new approximations, we propose nonoscillatory spectral methods which possess the properties of both upwind di erence schemes and spectral methods. Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed.

Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods.

The authors present numerical results for Cited by: 3. reconstruction is obtained. Next, the DOFs are updated to high-order accuracy using the usual Godunov method.

Numerical tests with scalar conservation laws in both 1D and 2D and 1D systems have verified that the SV method is indeed highly accurate, conservative, and geometrically flexible. Spectral Volume Method for the 2D Euler Equations The unsteady 2D Euler equation in.

unknowns. This is the main reason why high-order DG, SV and SD methods are more efficient than a high-order finite volume method. The SD formulation is similar to the pseudo-spectral or collocation spectral method16 in that both employ nodal solutions as the DOFs and both formulations are based on the differential form of the governing Size: KB.

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (), and provides an overview of the depth and breadth of the activities within this important research area. One-dimensional Euler equations The system of Euler equations for polytropic gas in one dimension is given by u, + f(u).~ = O, with (1) u =, f= um + P, (2) Lu(P + E)_J (if) P=(3'-l) E 5 ' (3) where p denotes density, u is velocity, P pressure, E total energy, m = pu is the momentum and 3, is the ratio of the specific heats of a polytropic by: 7.

In order to present basic ideas in the easiest way to understand fashion, the following scalar wave equation is often considered:(7)∂u∂t+∇(ua⇒)≡∂u∂t+a⇒∇u=0,where uis a (scalar) state variable, and a⇒is the wave velocity by: AUSM-Based High-Order Solution for Euler Equations Conference Paper in Communications in Computational Physics 12(4) January with 79 Reads How we measure 'reads'.

() L1 Fourier spectral methods for a class of generalized two-dimensional time fractional nonlinear anomalous diffusion equations. Computers & Mathematics with Applications() A high-order fully conservative block-centered finite difference method for the time-fractional advection–dispersion by: W.

Cai and C.-W. Shu, Uniform high-order spectral methods for one- and two-dimensional Euler equations, Journal of Computational Physics, v (), pp W. E and C.-W. Shu, Effective equations and the inverse cascade theory for Kolmogorov flows.

Cai and C.-W. Shu, Uniform high-order spectral methods for one- and two-dimensional Euler equations, Journal of Computational Physics, v (), pp W. E and C.-W. Shu, Effective equations and the inverse cascade theory for Kolmogorov flows, Physics of Fluids A, v5 (), pp W.

E and C.-W. Shu, A numerical File Size: KB. The papers presented in this section of the book show how extensively spectral methods have changed since the development over twenty years ago of transform methods Spectral Method Spectral Element Spectral Element Method Euler System W.

Cai and C. Shu. Uniform high order spectral methods for one and two dimensional Euler equations. Author: George Em Karniadakis, Steven A. Orszag. We consider several seconder order in time stabilized semi-implicit Fourier spectral schemes for 2D Cahn–Hilliard equations.

We introduce new stabilization techniques and prove unconditional energy stability for modified energy functionals. We also carry out a comparative study of several classical stabilization schemes and identify the corresponding stability by: This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods.

It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport Brand: Springer Netherlands.

Abstract. Finite spectral method is a conception of pointwise or cellwise local spectral schemes based on non-periodic Fourier transform. The method of non-periodic Fourier transform and two finite spectral schemes are presented.

Numerical tests of a wave propagation problem and a shock tube problem Cited by: A high-order exponential ADI scheme for two dimensional time fractional convection-diffusion equations Article in Computers & Mathematics with Applications 68(3) August with Reads.

() A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations. Applied Mathematics and Computation() Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger by: Least-Squares Spectral Element Method Applied to the Euler Equations Article in International Journal for Numerical Methods in Fluids 57(9) July with 71 Reads How we measure 'reads'.

Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations. A hybrid pressure–density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method.

High-Order Methods for Three-Dimensional Cited by:. 3 Systems of differential equations 37 Higher-order differential equations 39 Numerical methods for systems 42 Problems 46 4 The backward Euler method and the trapezoidal method 49 The backward Euler method 51 The trapezoidal method 56 Problems 62 5 Taylor and Runge–Kutta methods 67 Taylor methods 68 Runge–Kutta File Size: 1MB.() Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation.

Journal of Computational Physics() Numerical Algorithm With High Spatial Accuracy for the Fractional Diffusion Cited by: To cite this Article Mittal, R. C. and Jiwari, Ram()'Differential Quadrature Method for Two-Dimensional Burgers' Equations',International Journal for Computational Methods in Engineering.