کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6929096 1449355 2018 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes
چکیده انگلیسی
In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 358, 1 April 2018, Pages 21-35
نویسندگان
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