Transactions of Nanjing University of Aeronautics & Astronautics
A New D-GCL for Unidirectional Motion with Large Displacement
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Abstract:
Numerical simulations of unsteady flow problems with moving boundaries commonly require the use of geometric conservation law (GCL). However, in cases of unidirectional large mesh deformation, the cumulative error caused by the discrete procedure in GCL can significantly increase, and a direct consequence is that the calculated cell volume may become negative. To control the cumulative error, a new discrete GCL (D-GCL ) is proposed. Unlike the original D-GCL, the proposed method uses the control volume analytically evaluated according to the grid motion at the time level n, instead of using the calculated value from the D-GCL itself. Error analysis indicates that the truncation error of the numerical scheme is guaranteed to be the same order as that obtained from the original D-GCL, while the accumulated error is greatly reduced. For validation, two challenging large deformation cases including a rotating circular cylinder case and a descending GAW-(1) two-element airfoil case are selected to be investigated. Good agreements are found between the calculated results and some other literature data, demonstrating the feasibility of the proposed D-GCL for unidirectional motions with large displacements.
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