Abstract
There is often a need to compute flows containing regions in which the total energy is overwhelmingly dominated by the kinetic energy mode. This poses a difficulty if the equations are solved in conservation form. Pressure, being a difference of two large quantities, may be contaminated by various types of numerical error, and its value may become negative. It is also possible for a particular scheme to produce negative density even if an exact solution does not contain vacuum zones. As soon as density or pressure become negative a computation fails. When the problem occurs, it can be usually postponed by lowering the time step. However, one needs a scheme that preserves positivity for all time, under conditions not much more severe that the usual CFL restriction. This problem has recently received growing attention in the literature.
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Linde, T., Roe, P.L. (1998). On Multidimensional Positively Conservative High-Resolution Schemes. In: Venkatakrishnan, V., Salas, M.D., Chakravarthy, S.R. (eds) Barriers and Challenges in Computational Fluid Dynamics. ICASE/LaRC Interdisciplinary Series in Science and Engineering, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5169-6_16
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DOI: https://doi.org/10.1007/978-94-011-5169-6_16
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