Stability analysis of time stepping for prolonged plasma fluid simulations. (English) Zbl 1251.76067
Summary: The Hasegawa-Wakatani system of equations may be used to predict and study the behavior of plasma flow. Stability analysis of the flow requires results over prolonged time series, which places a great strain on computational resources. Results can only be achieved for a wide choice of parameters by using numerical methods that allow long time steps and do not pollute the results with numerical instabilities. The report presents an analysis of several linear multistep methods and concludes that much of the understanding of the stability of linear systems also applies to the study of nonlinear problems such as the Hasegawa-Wakatani system of equations. In particular, methods such as the backward differentiation formulas should be used with the stiff systems generated by the discrete formulation of the Hasegawa-Wakatani system of equations.
MSC:
76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
76M25 | Other numerical methods (fluid mechanics) (MSC2010) |