کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6932252 867719 2014 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Numerical integration techniques for discontinuous manufactured solutions
ترجمه فارسی عنوان
تکنیک های ادغام عددی برای راه حل های تولید نشده
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
When applying the method of manufactured solutions (MMS) on computational fluid dynamic software, determining the exact solutions and source terms for finite volume codes where the stored value is an integrated average over the control volume is non-trivial and not frequently discussed. MMS with discontinuities further complicates the problem of determining these values. In an effort to adapt the standard MMS procedure to solutions that contain discontinuities we show that Newton-Cotes and Gauss quadrature numerical integration methods exhibit high error, first order limitations. We propose a new method for determining the exact solutions and source terms on a uniform structured grid containing shock discontinuities by performing linearly and quadratically exact transformations on split cells. Transformations are performed on triangular and quadrilateral elements of a systematically divided discontinuous cell. Using a quadratic transformation in conjunction with a nine point Gauss quadrature method, a minimum of 4th order accuracy is achieved for fully general solutions and shock shapes. A linear approximation of curved shocks is also experimentally shown to be 2nd order accurate. The numerical integration method is then applied to a CFD code using simple discontinuous manufactured solutions which return consistent 1st order convergence values. The result is an important step towards being able to use MMS to verify solutions with discontinuities. This work also highlights the use of higher order numerical integration techniques for continuous and discontinuous solutions that are required for MMS on higher order finite volume codes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 278, 1 December 2014, Pages 193-203
نویسندگان
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