Verification of a Higher-Order Finite Difference Scheme for the One-Dimensional Two-Fluid Model

The one-dimensional two-fluid model is widely acknowledged as the most detailed and accurate macroscopic formulation model of the thermo-fluid dynamics in nuclear reactor safety analysis. Currently the prevailing one-dimensional thermal hydraulics codes are only first-order accurate. The benefit of first-order schemes is numerical viscosity, which serves as a regularization mechanism for many otherwise ill-posed two-fluid models. However, excessive diffusion in regions of large gradients leads to poor resolution of phenomena related to void wave propagation. In this work, a higher-order shock capturing method is applied to the basic equations for incompressible and isothermal flow of the one-dimensional two-fluid model. The higher-order accuracy is gained by a strong stability preserving multi-step scheme for the time discretization and a minmod flux limiter scheme for the convection terms. Additionally the use of a staggered grid allows for several second-order centered terms, when available. The continu...

[1]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[2]  P. Lax.  Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .

[3]  William J. Rider,et al.  On sub-linear convergence for linearly degenerate waves in capturing schemes , 2008, J. Comput. Phys..

[4]  H. Deconinck,et al.  Design principles for bounded higher-order convection schemes - a unified approach , 2007, J. Comput. Phys..

[5]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[6]  Timothy G. Trucano,et al.  Verification and validation. , 2005 .

[7]  Steinar Evje,et al.  Hybrid flux-splitting schemes for a common two-fluid model , 2003 .

[8]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[9]  J. A. Trapp,et al.  A discrete particle model for bubble-slug two-phase flows , 1993 .

[10]  M. Ishii,et al.  Thermo-Fluid Dynamics of Two-Phase Flow , 2007 .

[11]  Dimitri Gidaspow.  MODELING OF TWO PHASE FLOW , 1974 .

[12]  Yohsuke Imai,et al.  A higher-order implicit IDO scheme and its CFD application to local mesh refinement method , 2006 .

[13]  G. Wallis.  One Dimensional Two-Phase Flow , 1969 .

[14]  Washington,et al.  RELAP5/MOD3 code manual: Code structure, system models, and solution methods. Volume 1 , 1995 .

[15]  J. H. Stuhmiller,et al.  The influence of interfacial pressure forces on the character of two-phase flow model equations , 1977 .

[16]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[17]  P. Roe.  CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[18]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[19]  M. Ishii.  Thermo-fluid dynamic theory of two-phase flow , 1975 .

[20]  Jean-Michel Ghidaglia,et al.  On the numerical solution to two fluid models via a cell centered finite volume method , 2001 .