کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
522792 867860 2008 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A class of residual distribution schemes and their relation to relaxation systems
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A class of residual distribution schemes and their relation to relaxation systems
چکیده انگلیسی

Residual distributions (RD) schemes are a class of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed to the piecemeal 1D Riemann solvers usually employed by finite volume methods. In 1D, LeVeque and Pelanti [R.J. LeVeque, M. Pelanti, A class of approximate Riemann solvers and their relation to relaxation schemes, J. Comput. Phys. 172 (2001) 572] showed that many of the standard approximate Riemann solver methods (e.g., the Roe solver, HLL, Lax-Friedrichs) can be obtained from applying an exact Riemann solver to relaxation systems of the type introduced by Jin and Xin [S. Jin, Z.P. Xin, Relaxation schemes for systems of conservation-laws in arbitrary space dimensions, Commun. Pure Appl. Math. 48 (1995) 235]. In this work we extend LeVeque and Pelanti’s results and obtain a multidimensional relaxation system from which multidimensional approximate Riemann solvers can be obtained. In particular, we show that with one choice of parameters the relaxation system yields the standard N-scheme. With another choice, the relaxation system yields a new Riemann solver, which can be viewed as a genuinely multidimensional extension of the local Lax-Friedrichs scheme. This new Riemann solver does not require the use Roe–Struijs–Deconinck averages, nor does it require the inversion of an m × m matrix in each computational grid cell, where m is the number of conserved variables. Once this new scheme is established, we apply it on a few standard cases for the 2D compressible Euler equations of gas dynamics. We show that through the use of linear-preserving limiters, the new approach produces numerical solutions that are comparable in accuracy to the N-scheme, despite being computationally less expensive.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 227, Issue 22, 20 November 2008, Pages 9527–9553
نویسندگان
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