Abstract
Recall that one-sided methods cannot be used for systems of equations with eigenvalues of mixed sign. For a linear system of equations we previously obtained a natural generalization of the upwind method by diagonalizing the system, yielding the method (10.60). For nonlinear systems the matrix of eigenvectors is not constant, and this same approach does not work directly. In this chapter we will study a generalization in which the local characteristic structure, now obtained by solving a Riemann problem rather than by diagonalizing the Jacobian matrix, is used to define a natural upwind method. This method was first proposed for gas dynamics calculations by Godunov[24l.
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© 1992 Springer Basel AG
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LeVeque, R.J. (1992). Godunov’s Method. In: Numerical Methods for Conservation Laws. Lectures in Mathematics ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8629-1_13
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DOI: https://doi.org/10.1007/978-3-0348-8629-1_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2723-1
Online ISBN: 978-3-0348-8629-1
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