TY - JOUR
T1 - Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids
AU - Nonomura, Taku
AU - Iizuka, Nobuyuki
AU - Fujii, Kozo
N1 - Funding Information:
The authors are grateful to Associate Professor Ryoji Takaki and Assistant Professor Akira Oyama for their remarks on a draft of this paper. The first author is also grateful for the partial support of the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for JSPS Fellows, 19-3209 , 2007.
PY - 2010/2
Y1 - 2010/2
N2 - Freestream and vortex preservation properties of a weighted essentially nonoscillatory scheme (WENO) and a weighted compact nonlinear scheme (WCNS) on curvilinear grids are investigated. While the numerical technique used for the compact difference scheme can be applied to WCNS, applying it to WENO is difficult. This difference is caused by difference in the formulation of numerical fluxes. WENO computed in the generalized coordinate system does not work well for either freestream or vortex preservation, whereas WENO computed in the Cartesian coordinate system works well for both freestream and vortex preservation, but its resolution is lower than that of WCNS. In addition, WENO in the Cartesian coordinate system costs three times as much as WENO or WCNS in the generalized coordinate system. Therefore, WENO in the Cartesian coordinate system is not suitable for solving Euler equations on a curvilinear grid. On the other hand, WCNS computed in the generalized coordinate system works well for freestream and vortex preservation when used with the numerical technique proposed for the compact difference scheme. The results show that WCNS with this numerical technique can be used for an arbitrary grid system. In this paper, the excellent freestream and vortex preservation properties of WCNS when used with the numerical technique, compared with those of WENO, are shown for the first time.
AB - Freestream and vortex preservation properties of a weighted essentially nonoscillatory scheme (WENO) and a weighted compact nonlinear scheme (WCNS) on curvilinear grids are investigated. While the numerical technique used for the compact difference scheme can be applied to WCNS, applying it to WENO is difficult. This difference is caused by difference in the formulation of numerical fluxes. WENO computed in the generalized coordinate system does not work well for either freestream or vortex preservation, whereas WENO computed in the Cartesian coordinate system works well for both freestream and vortex preservation, but its resolution is lower than that of WCNS. In addition, WENO in the Cartesian coordinate system costs three times as much as WENO or WCNS in the generalized coordinate system. Therefore, WENO in the Cartesian coordinate system is not suitable for solving Euler equations on a curvilinear grid. On the other hand, WCNS computed in the generalized coordinate system works well for freestream and vortex preservation when used with the numerical technique proposed for the compact difference scheme. The results show that WCNS with this numerical technique can be used for an arbitrary grid system. In this paper, the excellent freestream and vortex preservation properties of WCNS when used with the numerical technique, compared with those of WENO, are shown for the first time.
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U2 - 10.1016/j.compfluid.2009.08.005
DO - 10.1016/j.compfluid.2009.08.005
M3 - Article
AN - SCOPUS:70350716288
VL - 39
SP - 197
EP - 214
JO - Computers and Fluids
JF - Computers and Fluids
SN - 0045-7930
IS - 2
ER -