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PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Nonlinear Flux Approximation Scheme for Burgers Equation Derived from a Local BVP

Authors : J. H. M. ten Thije Boonkkamp, N. Kumar, B. Koren, D. A. M. van der Woude, A. Linke

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

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Abstract

We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.

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previous chapter Galerkin Projection and Numerical Integration for a Stochastic Investigation of the Viscous Burgers’ Equation: An Initial Attempt
next chapter A Spectral Solenoidal-Galerkin Method for Flow Past a Circular Cylinder
Literature
1.
J.M. Burgers, A Mathematical Model Illustrating the Theory of Turbulence (Academic Press, New York, 1948)CrossRef
2.
R. Eymard, T. Gallouët, R. Herbin, Finite volume methods, in Handbook of Numerical Analysis, ed. by P.G. Ciarlet, J.L. Lions, vol. VII (North-Holland, Amsterdam, 2000), pp. 713–1020
3.
R. Eymard, J. Fuhrmann, K. Gärtner, A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems. Numer. Math. 102, 463–495 (2006)MathSciNetCrossRef
4.
N. Kumar, Flux approximation schemes for flow problems using local boundary value problems, PhD Thesis, Eindhoven University of Technology, 2017
5.
N. Kumar, J.H.M. ten Thije Boonkkamp, B. Koren, A. Linke, A nonlinear flux approximation scheme for the viscous Burgers equation, in Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, ed. by C. Cances, P. Omnes (Springer, Switzerland, 2017), pp. 457–465CrossRef
6.
J.H.M. ten Thije Boonkkamp, M.J.H. Anthonissen, The finite volume-complete flux scheme for advection-diffusion-reaction equations. J. Sci. Comput. 46, 47–70 (2011)MathSciNetCrossRef
Metadata
Title
Nonlinear Flux Approximation Scheme for Burgers Equation Derived from a Local BVP
Authors
J. H. M. ten Thije Boonkkamp
N. Kumar
B. Koren
D. A. M. van der Woude
A. Linke
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_96

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