Titlebook: Numerical Methods for Conservation Laws; Randall J. LeVeque Textbook 1992Latest edition Springer Basel AG 1992 CFL condition.average.compa

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IntroductionThese notes concern the solution of hyperbolic systems of conservation laws. These are time-dependent systems of partial differential equations (usually nonlinear) with a particularly simple structure.

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Scalar Conservation LawsWe begin our study of conservation laws by considering the scalar case. Many of the difficulties encountered with systems of equations are already encountered here, and a good understanding of the scalar equation is required before proceeding.

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Rarefaction Waves and Integral CurvesAll of the Riemann solutions considered so far have the following property: the solution is constant along all rays of the form . = ξ.. Consequently, the solution is a function of ./. alone, and is said to be a “similarity solution” of the PDE.

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Numerical Methods for Linear EquationsBefore studying numerical methods for nonlinear conservation laws, we review some of the basic theory of numerical methods for the linear advection equation and linear hyperbolic systems. The emphasis will be on concepts that carry over to the nonlinear case.

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