TY - JOUR

T1 - EFFICIENT TIME-MARCHING SCHEME FOR SOLVING COMPRESSIBLE EULER EQUATIONS.

AU - Daiguji, Hisaaki

AU - Yamamoto, Satoru

PY - 1986

Y1 - 1986

N2 - An implicit time-marching finite-difference scheme is proposed for analyzing steady two-dimensional inviscid transonic flows. The scheme is based on the well-known Beam-Warming delta-form approximate factorization scheme, but this is improved in the following two points: (i) In order to treat the fixed wall boundary condition without difficulty, momentum equations of contravariant velocity components as fundamental equations in curvilinear coordinates are used. (ii) To calculate stably with a sufficiently large Courant number, the central-difference of the Crank-Nicholson method is replaced by the upsteam-difference of the Robert-Weiss method. The upstreaming is performed on the basis of the theory of characteristics and does not influence the accuracy of the solution. The flows through a converging-diverging nozzle and a symmetric wing are calculated. The calculated results agree well with the existing theories.

AB - An implicit time-marching finite-difference scheme is proposed for analyzing steady two-dimensional inviscid transonic flows. The scheme is based on the well-known Beam-Warming delta-form approximate factorization scheme, but this is improved in the following two points: (i) In order to treat the fixed wall boundary condition without difficulty, momentum equations of contravariant velocity components as fundamental equations in curvilinear coordinates are used. (ii) To calculate stably with a sufficiently large Courant number, the central-difference of the Crank-Nicholson method is replaced by the upsteam-difference of the Robert-Weiss method. The upstreaming is performed on the basis of the theory of characteristics and does not influence the accuracy of the solution. The flows through a converging-diverging nozzle and a symmetric wing are calculated. The calculated results agree well with the existing theories.

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U2 - 10.1299/jsme1958.29.2845

DO - 10.1299/jsme1958.29.2845

M3 - Article

AN - SCOPUS:0022780468

SN - 0021-3764

VL - 29

SP - 2845

EP - 2850

JO - Bulletin of the JSME

JF - Bulletin of the JSME

IS - 255

ER -