New Approaches for Reducing Artificial Oscillations in Numerical Solutions. Anti-Diffusion, Anti-Dispersion and Longoliers
Two most known errors is the artificial smoothing of the solution and oscillations in the solutions near the places with high derivatives of the solutions (near the sharp fronts of the solution). Some methods of improving numerical solutions of evolution equations are proposed on the base of theoret...
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| Datum: | 2019 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Кам'янець-Подільський національний університет імені Івана Огієнка
2019
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| Online Zugang: | http://mcm-math.kpnu.edu.ua/article/view/174183 |
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| Назва журналу: | Mathematical and computer modelling. Series: Physical and mathematical sciences |
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Mathematical and computer modelling. Series: Physical and mathematical sciences| Zusammenfassung: | Two most known errors is the artificial smoothing of the solution and oscillations in the solutions near the places with high derivatives of the solutions (near the sharp fronts of the solution). Some methods of improving numerical solutions of evolution equations are proposed on the base of theoretical considerations. The artificial viscosity and artificial dispersion for difference schemes of gas dynamics are proposed as the first examples. A new class of tools for improving numerical solutions is proposed — «Langoliers». «Langoliers» are special difference operators which should be applied at each time steps after the running of original difference schemes. The design of «Langoliers» allows reducing the dissipative and dispersive errors of schemes. The examples are anti-diffusion, anti-dispersion and specially constructed difference schemes |
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