Improvement of accuracy and stability in numerically solving hyperbolic equations by IDO (Interpolated Differential Operator) scheme with Runge-Kutta time integration

Yoshida, Hiroshi*; Aoki, Takayuki*; Utsumi, Takayuki*

Denshi Joho Tsushin Gakkai Rombunshi, A, 86(3), p.223 - 231, 2003/03

https://ci.nii.ac.jp/naid/110003311635

no abstracts in English

New numerical method for the solutions of the MCDF equations based on the CIP method

Utsumi, Takayuki*; Koga, J. K.

Computer Physics Communications, 148(3), p.281 - 290, 2002/11

https://doi.org/10.1016/S0010-4655(02)00597-0

no abstracts in English

1D plasma simulation in phase space with the differential algebraic cubic interpolated propagation scheme

Computational Fluid Dynamics Journal, 8(1), p.135 - 141, 1999/04

no abstracts in English

Study of thermal-hydraulic analyses with CIP method

PNC TN9420 96-057, 48 Pages, 1996/09

PNC-TN9420-96-057.pdf:1.24MB

New type of numerical scheme CIP has been proposed for solving hyperbolic type equations and the CIP is focused on as a less numerical diffusive scheme. C-CUP method with the CIP scheme is adopted to numerical simulations that treat compressible and incompressible fluids, phase change phenomena and Mixture fluids. To evaluate applicabilities of the CIP scheme and C-CUP method for thermal hydraulic analyses related to Fast Breeder Reactors (FBRs), the scheme and the method were reviewed. Feature of the CIP scheme and procedure of the C-CUP method were presented. The CIP scheme is used to solve linear hyperbolic type equations for advection term in basic equations of fluids. Key issues of the scheme is that profile between grid points is described to solve the equation by cubic polynomial and spatial derivatives of the polynomial. The scheme can capture steep change of solution and suppress numerical error. In the C-CUP method, the basic equations of fluids are divided into advection terms and the other terms. The advection terms is solved with CIP scheme and the other terms is solved with difference method.The C-CUP method is robust for numerical instability, but mass of fluid will be in unfair preservation with non-conservative equations for fluids. Numerical analyses with the CIP scheme and the C-CUP method has been performed for phase change, mixture and moving object. These analyses are depend on characteristics of that the scheme and the method are robust for steep change of density and useful for interface tracking.