By K. R. Arun, M. Lukáčová-Medvidová (auth.), Rainer Ansorge, Hester Bijl, Andreas Meister, Thomas Sonar (eds.)
In January 2012 an Oberwolfach workshop came about related to recent
developments within the numerics of partial differential equations. concentration was once laid
on equipment of excessive order and on functions in Computational Fluid Dynamics. The ebook covers many of the talks provided at this workshop.
Read or Download 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 PDF
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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
Sample text
3 Operator spectrum for polynomial advection speed and N = 15 with different number of integration points. The right plot shows a zoomed view of the imaginary axis. 6E − 6 0 0 j real part moves closer to the imaginary axis. For N + 14 = 29 integration points and above, the real parts of the eigenvalues are not positive anymore, resulting in a stable de-aliased approximation. 3 Sinusoidal Advection Velocity The last test case are the non-polynomial functions a(x) = 1 2 2 + sin 2π x + sin 3π x , 2 3 a(x) = 1 2 8 2+ ∑ j=2 14 sin jπ x , 5j (13a) (13b) where (13b) is just a slight modification of (13a) with additional higher frequency terms and a weaker decay of amplitudes.
Numer. Anal. 27, 1405–1421 (1990) 21. : Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM J. Numer. Anal. R. Arun et al. 22. : A simple multidimensional relaxation scheme based on characteristics and interpolation. In: 16th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, June 23-26. American Institute of Aeronautics and Astronautics, AIAA-2003-3535 (2003) 23. : Efficient implementation of essentially non-oscillatory shockcapturing schemes II.
The results of first order scheme are highly smeared due the excess amount of numerical diffusion. The second order scheme is comparatively much less dissipative and it resolves the discontinuities very well. Lax Shock Tube Problem. This test case is the Lax shock tube problem. 5 < x ≤ 1. 9. 8 1 x−axis Fig. 13. The plots show that the second order scheme gives a sharper resolution of both shocks and expansions. Strong Rarefactions Riemann Problem. 5 < x ≤ 1. This is a very difficult problem for many methods because a near vacuum state is reached and failure can occur as a result of negative densities or pressures.