کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4967088 1449363 2017 44 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows
ترجمه فارسی عنوان
روشهای تلفیقی زمانهای مشتق شده برای حلقههای گالکینک فشرده نشده
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
In this paper we investigate the possibility of using the high-order accurate A(α)-stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 350, 1 December 2017, Pages 493-517
نویسندگان
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