TY - GEN
T1 - On the discretization of spatial metrics satisfying the GCL identities
AU - Abe, Y.
AU - Nonomura, T.
AU - Iizuka, N.
AU - Fujii, K.
PY - 2012/12/1
Y1 - 2012/12/1
N2 - In this research, the spatial metrics used in the finite difference scheme for curvilinear coordinate system are discussed from the viewpoint of geometric interpretation. We summarized all the evaluation technique for second-order metrics proposed in the previous studies, and explain their geometric interpretation if they have appropriate geometries. Adoptingthe regular second-order finite difference scheme, only the symmetric conservative formulation has the appropriate geometry in the viewpoint of finite volume scheme. This form straightforwardly extended to the high order scheme, having appropriate geometry interpretations. This form improves the robustness of the high-order computation on the highly skewed grids compared with the asymmetric conservative formulation which is often used in the fluidic computation.
AB - In this research, the spatial metrics used in the finite difference scheme for curvilinear coordinate system are discussed from the viewpoint of geometric interpretation. We summarized all the evaluation technique for second-order metrics proposed in the previous studies, and explain their geometric interpretation if they have appropriate geometries. Adoptingthe regular second-order finite difference scheme, only the symmetric conservative formulation has the appropriate geometry in the viewpoint of finite volume scheme. This form straightforwardly extended to the high order scheme, having appropriate geometry interpretations. This form improves the robustness of the high-order computation on the highly skewed grids compared with the asymmetric conservative formulation which is often used in the fluidic computation.
KW - Conservative form
KW - Geometric conservation law
KW - Geometric interpretation
KW - High order scheme
KW - SCL identity
KW - Spatial metrics
UR - http://www.scopus.com/inward/record.url?scp=84871629967&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:84871629967
SN - 9783950353709
T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
SP - 3575
EP - 3594
BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Y2 - 10 September 2012 through 14 September 2012
ER -