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- W2137003322 abstract "A trademark of nonlinear, time-dependent, convection-dominated prob lems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution computations. We overview recent developments of modern computational methods for the approximate solution of such problems. In these computations, one seeks piecewise smooth solutions which are realized by finite dimensional projections. Computational methods in this context can be classified into two main categories, of local and global methods. Local methods are expressed in terms of point-values (— Hamilton-Jaco bi equa tions), cell averages (— nonlinear conservation laws), or higher focalized mo ments. Global methods are expressed in terms of global basis functions. High resolution central schemes will be discussed as a prototype example for local methods. The family of central schemes offers high-resolution blackbox-solvers to an impressive range of such nonlinear problems. The main in gredients here are detection of spurious extreme values, non-oscillatory recon struction in the directions of smoothness, numerical dissipation and quadra ture rules. Adaptive spectral viscosity will be discussed as an example for high-resolution global methods. The main ingredients here are detection of edges in spectral data, separation of scales, adaptive reconstruction, and spec tral viscosity." @default.
- W2137003322 created "2016-06-24" @default.
- W2137003322 creator A5072355478 @default.
- W2137003322 date "2002-01-01" @default.
- W2137003322 modified "2023-09-27" @default.
- W2137003322 title "High Resolution Methods for Time Dependent Problems with Piecewise Smooth Solutions" @default.
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