Titlebook: Numerical Methods for Conservation Laws; Randall J. LeVeque Book 19901st edition Birkhäuser Basel 1990 numerical method.research.shock wav

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Some Scalar Examplesvious chapter. The first of these examples (traffic flow) should also help develop some physical intuition that is applicable to the more complicated case of gas dynamics, with gas molecules taking the place of cars. This application is discussed in much more detail in Chapter 3 of Whitham[97]. The

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The Riemann problem for the Euler equationst the details are messier. Instead, I will concentrate on discussing one new feature seen here, contact discontinuities, and see how we can take advantage of the linear degeneracy of one field to simplify the solution process for a general Riemann problem. Full details are available in many sources,

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Godunov’s Methodbtained 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 character

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Semi-discrete Methodsation process in two stages, first discretizing only in space, leaving the problem continuous in time. This leads to a system of ordinary differential equations in time, called the “semi-discrete equations”. We then discretize in time using any standard numerical method for systems of ordinary diffe

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