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Computing Qualitatively Correct Approximations of Balance Laws pp 315–321Cite as

Conclusion: Outlook and Shortcomings

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Abstract

The so-called method of artificial viscosity has been introduced in the seminal 1950 paper by Richtmyer and Von Neumann [24], where a Lagrangian hyperbolic system of gas dynamics is approximated by finite differences on staggered grids (the specific volume and the velocity aren’t known at the same points). In order to stabilize the Fourier modes of the numerical solution, it appeared necessary to include an artificial dissipative term in the pressure law, negligible in smooth areas and \( \mathcal{O} \)(1) in the vicinity of shocks. On the contrary [11], scientists in the Soviet Union

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  1. Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR, Rome, Italy

    Laurent Gosse

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  1. Laurent Gosse
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Gosse, L. (2013). Conclusion: Outlook and Shortcomings. In: Computing Qualitatively Correct Approximations of Balance Laws. SIMAI Springer Series, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2892-0_16

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