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Title A low-dissipation, limited second-order scheme for use with finite volume computational fluid dynamics simulations
Publication Date
Degree PhD
Discipline/Department Mechanical Engineering
Degree Level doctoral
University/Publisher Mississippi State University
Abstract Finite volume methods employing second-order gradient reconstruction schemes are often utilized to computationally solve the governing equations of fluid mechanics and transport. These schemes, while not as dissipative as first-order schemes, frequently produce oscillatory solutions in regions of discontinuities and/or unsatisfactory levels of dissipation in smooth regions of the variable field. Limiters are often employed to reduce the inherent variable over- and under-shoot; however, they can significantly increase the numerical dissipation of a solution, eroding a schemes performance in smooth regions. A novel gradient reconstruction scheme, which shows significant improvement over traditional second-order schemes, is presented in this work. Two implementations of this Optimization-based Gradient REconstruction (OGRE) scheme are examined: minimizing an objective function based on the mismatch between local reconstructions at midpoints or selected quadrature points between cell stencil neighbors. Regardless of the implementation employed, the resulting gradient calculation is a compact, implicit method that can be used with unstructured meshes by employing an arbitrary computational stencil. An adjustable weighting parameter is included in the objective function that allows the scheme to be tuned towards either greater accuracy or greater stability. To address over- and undershoot of the variable field near discontinuities, non-local, non-monotonic (NLNM) and local, non-monotonic (LNM) limiters have also been developed, which operate by enforcing cell minima and maxima on dependent variable values projected to cell faces. The former determines minimum and maximum values for a cell through recursive reference to the minimum and maximum values of its upwind neighbors. The latter determines these bounding values through examination of the extrema of values of the dependent variable projected from the face-neighbor cell into the original cell. Steady state test cases on structured and unstructured grids are presented, exhibiting the low-dissipative nature of the scheme. Results are primarily compared to those produced by existing limited and unlimited second-order upwind (SOU) and first-order upwind (FOU). Solution accuracy, convergence rate and computational costs are examined.
Subjects/Keywords local; non-monotonic; optimization; non-local; gradient reconstruction; finite volume; dissipation; CFD; low dissipation; computational fluid dynamics; limiter; second order scheme
Contributors D. Keith Walters (chair); B. Keith Hodge (committee_member); Rogelio Luck (committee_member); David S. Thompson (committee_member)
Language en
Rights unrestricted
Country of Publication us
Format application/pdf
Record ID oai:library.msstate.edu:etd-03282013-224608
Repository msstate
Date Retrieved
Date Indexed 2018-01-03

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