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Thursday, July 16, 2020 | History

3 edition of Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation found in the catalog.

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

J. Liandrat

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

by J. Liandrat

  • 8 Want to read
  • 4 Currently reading

Published by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, For sale by the National Technical Information Service in Hampton, Va, [Springfield, Va .
Written in English

    Subjects:
  • Boundary conditions.,
  • Burger equation.,
  • Coefficients.,
  • Degrees of freedom.,
  • Linear operators.,
  • Time marching.,
  • Trees (Mathematics)

  • Edition Notes

    StatementJ. Liandrat, Ph. Tchamitchian.
    SeriesICASE report -- no. 90-83., NASA contractor report -- 187480., NASA contractor report -- NASA CR-187480.
    ContributionsTchamitchian, Philippe., Institute for Computer Applications in Science and Engineering.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL16128789M

    In this article, we propose a method for the solution of the generalized Burger–Fisher equation. The method is developed using CAS wavelets in conjunction with quasi-linearization technique. The operational matrices for the CAS wavelets are derived and constructed. AMSC 2D Spectral Element Scheme for Viscous Burgers’ Equation 10 Time Discretization For spectral methods the eigenvalues, λ, of the diffusion matrix are real and negative, and the maximum eigenvalue is O(N4)where N is the maximum polynomial degree.

    An example of stable model reduction for the Burger’s equation using closure models is explored in [4], [5]. These closure models modify some stability-enhancing coefficients of the reduced order ODE model using either constant additive terms, such as the constant eddy viscosity model, or time and space varying terms, such as Smagorinsky models. Propagation of sound. The wave equation () arises as the linear approximation of the compressible Euler equations, which describe the behavior of compressible uids (e.g., air). Gravitational wave. A suitable geometric generalization of the wave equation () turns out to be the linear approximation of the Einstein equations, which is the basic.

    Burgers equation from a theoretical viewpoint 8. The quan-tum Boltzmann equation 2 is derived from 1, and in turn the Burgers equation 6 is derived from 1 where the shear viscosity is found to be of the form 8 = 1 2z t cot2. 7 That the transport coefficient is a function of is a salient feature of the type-II quantum algorithmic method. As → 2. Solving the burgers' and regularized long wave equations using the new perturbation iteration technique. Necdet Bildik. Corresponding Author. E-mail address: @ This method is recovered and amended to solve the Burgers' and regularized long wave equations. Comparing our new solutions with the exact solutions reveals that.


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Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation by J. Liandrat Download PDF EPUB FB2

RESOLUTION OF THE 1D REGULARIZED BURGERS EQUATION USING A SPATIAL WAVELET APPROXIMATION J. Liandrat1 IMST 12 avenue g6n6ral Leclerc Marseille, France Ph.

Tchamitchian CPT-CNRS Luminy case Marseille, France and Facult6 Saint Jr6me Universit6 Aix -Marseille III. Marseille. France ABSTRACT. Get this from a library. Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation. [J Liandrat; Philippe Tchamitchian; Institute.

Full text of "Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation" See other formats NASA Contractor Report ICASE Report No.

^3 ICASE RESOLUTION OF THE ID REGULARIZED BURGERS EQUATION USING A SPATIAL WAVELET APPROXIMATION J. Liandrat Ph. The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets.

The 1D Burgers equation is solved using explicit spatial discretization (upwind and central difference) with periodic boundary conditions on the domain (0,2). The 2D case is solved on a square domain of 2X2 and both explicit and implicit methods are used for the diffusive terms.

Dirichlet boundary conditions are used along the edges of the s: 4. Basdevant C., Holschneider M., Liandrat J., Perrier V., Tchamitchian P. () Numerical resolution of the burgers equation using the wavelet transform. In: Morton K.W.

(eds) Twelfth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol Springer, Berlin, Heidelberg. First Online 27 August Multiresolution Solution of Burgers Equation with B-spl ine Wavelet Basis S. Hadi Seyedi a a Mechanical Engineering Department, Wayne State Univers ity, Detroit, MichiganUSA.

Recently, wavelet-based numerical methods have been newly developed in the areas of science and engineering. In this paper, we proposed a full-approximation scheme for the numerical solution of Burgers’ equation using biorthogonal wavelet filter coefficients as prolongation and.

In this paper, we study the solution of the Burgers’ equation, a non-linear Partial Differential equation, using Legendre wavelets based technique. Burgers’ equation is an essential partial differential equation from fluid mechanics and is also used extensively in other areas of engineering such as gas dynamics, traffic flow modeling, acoustic wave propagation, and so on.

In Section 2, a fully implicit finite-difference scheme for two-dimensional Burgers’ equations is presented. In Section 3, the analysis of the proposed discrete ADM is given. Some numerical results are provided in Section 4 to illustrate the method.

Section 5 concludes the paper. An implicit finite-difference form for Burgers’ equations. Burgers’s equation (1) u t + uu x = u xx is a successful, though rather simpli ed, mathematical model of the motion of a viscous compressible gas, where u= the speed of the gas, = the kinematic viscosity, x= the spatial coordinate, t= the time.

Solution of the Burgers equation with nonzero viscosity Let us look for a solution of Eq. Spectral and finite difference solutions of the Burgers equation, Computers and Fluids, Vol Number 1,pages Source Code: burgers_viscous_time_exact1.m, evaluates exact solution #1 to the Burgers equation.

burgers_viscous_time_exact2.m, evaluates exact solution #2 to the Burgers equation. The approximate solutions for the Burger's-Huxley and Burger's-Fisher equations are obtained by using the Adomian decomposition method (Solving Frontier Problems of Physics: the Decomposition.

General Solution of the 1D Burgers Equation We are now in the position to formulate the general solution of the Burgers equa-tion () in one spatial dimension with initial condition u(x,0), ψ(x,0)=e−21ν Rx dx ′u(x,0). () The solution of the 1D heat equation can be expressed by the heat-kernel ψ(x,t)= Z dx′G(x−x′,t)ψ(x.

Liandrat and P. Tchamitchian, Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation, NASA CR ICASE Report No. 90–83 (). Google Scholar; Y. Maday, V. Perrier and J. Ravel, Dynamical adaptivity using wavelets basis for the approximation of PDEs, C.

Acad. Sci. () –   Tchamitchian, Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation, NASA Report, ICASE Report,Google Scholar [12].

Viscous approximation: the Burgers equation 3. The inviscid limit Using the results on the heat equation together with the Hopf-Cole transformation, we get the existence of a unique solution u "to the Burgers equation (1) for any xed ">0, and any nice initial data u 0.

The next step is to describe the asymptotic behavior of u "as "!0. Proposition. Conjecture 1 The solution of the approximating equation (5) converges, as "!0, to the solution of du= @2 xudt [email protected] udt+ ˙2 4 a b a+ b dt+ ˙dw: (10) Thus, the approximation converges to the stochastic Burgers equation (4) only for a= b.

Remark The solution to the stochastic Burgers equation (or rather the integrated process. 1 sparsity under a wavelet transform.

It has been exploited that MR images are sparse both in the spatial nite di erences domain and under wavelet trans-form [21]. These properties have been successfully applied in MR reconstructions in compressive sensing [21].

In this paper we focus on the joint estimation and regularization of the ODF 2. A fast adaptive diffusion wavelet method is developed for solving the Burger’s equation. The diffusion wavelet is developed in (Coifman and Maggioni, ) and its most important feature is that it can be constructed on any kind of manifold.

TchamitchianResolution of the 1D regularized Burgers equation using a spatial wavelet. Ph. Tchamitchian's 14 research works with citations and 3, reads, including: On the fast approximation of some nonlinear operators in nonregular wavelet spaces. This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets.

The method is based on a second-order finite difference formula combined with the collocation method which uses the wavelet basis and applied to the Burgers equation. Performance and accuracy of the numerical solutions are studied using.

This work addresses, numerical method based on Haar wavelets and finite differences to solve two dimensional linear, nonlinear Sobolev and non-linear generalized Benjamin–Bona–Mahony–Burgers (NGBBMB) equations. The temporal part is discretized using finite differences while spatial part is approximated by two dimensional Haar wavelets.