Recent Developments in the Numerics of Nonlinear Hyperbolic by K. R. Arun, M. Lukáčová-Medvidová (auth.), Rainer Ansorge,

By K. R. Arun, M. Lukáčová-Medvidová (auth.), Rainer Ansorge, Hester Bijl, Andreas Meister, Thomas Sonar (eds.)

In January 2012 an Oberwolfach workshop happened regarding recent

developments within the numerics of partial differential equations. concentration was once laid

on equipment of excessive order and on purposes in Computational Fluid Dynamics. The ebook covers lots of the talks provided at this workshop.

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Extra info for Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws: Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 – 21, 2012

Example text

A third example is a so-called Energy Tower [9], where the driving force is the latent heat of water. The first and the latter example will be discussed in detail below. By slow we mean that the flow velocities are slow compared to the speed of sound. After describing the general setting of such type of problems we will focus on two examples. The first one is a chimney in which the physical behaviour is well known and the mathematical setting is simple enough to carry on our analysis in great details and discuss different kinds of possible asymptotic limits.

As can be seen for the constant advection speed, the integration precision is exact with N + 1 points and thus the spectrum does not change when increasing the number of integration points to 26. The maximum of the real parts of the eigenvalues is 0, confirming the stability of the DG operator. 45 N=15, Int Points=16 N=15, Int Points=26 30 Im(λj) 15 0 -15 -30 -45 -100 -50 0 Re(λj) Fig. 1 Operator spectrum for constant advection speed and N = 15 with either 16 or 26 integration points, respectively.

1 Constant Advection Velocity As the advection speed is a = 1 = constant, the flux function is a polynomial of degree N. Thus, using N + 1 Gauss points with integration precision 2N + 1 is sufficient to integrate it exactly. The corresponding spectrum of the DG operator for N = 15 is plotted in Fig. 1. As can be seen for the constant advection speed, the integration precision is exact with N + 1 points and thus the spectrum does not change when increasing the number of integration points to 26.

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