Abstract
Monotonic Difference Schemes: In one of his earliest papers concerned with numerical schemes for solving equations of Gas Dynamics Godunov (1959) seeks an alternative to the Method of Characteristics. He proposes three main requirements for such schemes. Firstly, they should retain the simplicity of Characteristics Methods while overcoming the inconveniences introduced by shearing and distortion of characteristics networks. Secondly, they should be able to include consideration of surfaces of discontinuity such as shock waves and fluid interfaces. Thirdly, when applied to linearized equations they should predict a solution for physical variables which is in qualitative agreement with analytical solutions.
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Holt, M. (1977). The Godunov Schemes. In: Numerical Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96370-4_2
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DOI: https://doi.org/10.1007/978-3-642-96370-4_2
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