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Compact finite-difference schemes for quasilinear conservation laws
P. 3–03.
Gordin V. A., Zhukova G. N.
Many physical phenomena (e.g., gas dynamics) are described by systems of quasi-linear PDE such as conservation laws. Since Richardson’s famous attempt a century ago, they have been used for weather forecasting. Of course, modern models include descriptions of a huge number of additional physical processes, starting with turbulent viscosity and phase transitions. But the most important block of numerical hydrodynamic weather forecast is still an effective solver for systems of conservation laws. In the simplest case, this is the Euler – Hopf equation: ∂tu + ∂x(u 2/2) = 0.
In book
Vol. 53. , Geneva: World Meteorological Organization, 2023.