کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4967546 | 1449378 | 2017 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
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چکیده انگلیسی
In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge-Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge-Kutta stages simultaneously. Numerical experiments are performed on the Navier-Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. The fully implicit Radau IIA Runge-Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix-vector multiplications, and wall-clock time, for a wide range of time steps.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 335, 15 April 2017, Pages 700-717
Journal: Journal of Computational Physics - Volume 335, 15 April 2017, Pages 700-717
نویسندگان
Will Pazner, Per-Olof Persson,