HYPERBOLIC CONSERVATION LAWS
This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the spectral/hp method whilst honouring the inherent monotonicity and conservation properties of the analytic system. Different ways of dealing with these fundamental issues for both the Euler and the Navier-Stokes equations are considered. A new section for the shallow water equations is also included and the section on the discontinuous Galerkin method has been rewritten. Finally, the last section discusses modeling of plasma flows, i.e., the so-called magneto-hydrodynamic (MHD) equations.
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