Abstract
This chapter is concerned with numerical methods for solving non-linear systems of hyperbolic conservation laws in multidimensions. For Cartesian geometries one may write the equations of our interest here as
where t denotes time or a time-like variable and x, y, z are Cartesian coordinate directions. U is the vector of conserved variables and F(U), G(U), H(U) are vectors of fluxes in the x, y, z directions respectively. A prominent example are the time-dependent three dimensional Euler equations studied in Sect. 3.2 of Chap. 3. Other examples are the time-dependent two dimensional shallow water equations and the artificial compressibility equations. See Sect. 1.6.3 of Chap. 1.
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© 1997 Springer-Verlag Berlin Heidelberg
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Toro, E.F. (1997). Methods for Multi-Dimensional PDEs. In: Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03490-3_16
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DOI: https://doi.org/10.1007/978-3-662-03490-3_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03492-7
Online ISBN: 978-3-662-03490-3
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