Extension of staggered-grid-based AUSM-family schemes for use in nuclear safety analysis codes

Abstract To overcome the numerical difficulties of the density-based method for low-Mach-number two-phase flow, this paper adopts the AUSM + and AUSMDV schemes based on a staggered-grid arrangement. The water faucet, air-water shock tube, oscillating manometer and air-water phase separation problems are used as benchmark tests to validate the implementation of the generic four-equation two-fluid model. The present results reveal the advantages of using staggered-grid-based AUSM + and AUSMDV schemes over the collocated-grid-based counterpart. With a staggered-grid arrangement, odd-even decoupling issues can be avoided. Thus, no sound speed scaling or additional diffusion terms are needed when using AUSM + and AUSMDV schemes for low-Mach-number two-phase flow. Furthermore, since the pressure and void fraction are already stored at the interface of the velocity control volume, no interpolation of interfacial pressure is needed for momentum equations. Finally, this study will help integrate AUSM + and AUSMDV schemes into staggered-grid-based thermal hydraulic codes, e.g. CATHENA, used in the nuclear industry. Moreover, to tackle the stiffness issues in relation to phase appearance and disappearance, we propose a new staggered-grid-based scheme referred to as AUSMFVS, which combines the accuracy of AUSM + and the stability of FVS.

[1]  Christophe Eric Corre,et al.  On the extension of the AUSM+ scheme to compressible two-fluid models , 2003 .

[2]  Steinar Evje,et al.  Hybrid flux-splitting schemes for a two-phase flow model , 2002 .

[3]  Keun-Shik Chang,et al.  Numerical Simulation of Two-Fluid Two-Phase Flows by HLL Scheme Using an Approximate Jacobian Matrix , 2006 .

[4]  Meng-Sing Liou,et al.  Simulation of Multifluid Multiphase Flows with AUSM+-up Scheme , 2006 .

[5]  H. Bruce Stewart,et al.  Two-phase flow: Models and methods , 1984 .

[6]  R. Abgrall.  How to Prevent Pressure Oscillations in Multicomponent Flow Calculations , 1996 .

[7]  B. N. Hanna,et al.  CATHENA: A thermalhydraulic code for CANDU analysis , 1998 .

[8]  M. Liou.  A Sequel to AUSM , 1996 .

[9]  Frédéric Coquel,et al.  A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows , 1997 .

[10]  Oh-Hyun Rho,et al.  Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme , 2001 .

[11]  José Ramón,et al.  Conservative numerical schemes for unsteady 1D two phase flow , 2009 .

[12]  V. H. Ransom.  NUMERICAL BENCHMARK TEST NO. 2.1: FAUCET FLOW , 1987 .

[13]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[14]  Yang-Yao Niu,et al.  A further work on multi‐phase two‐fluid approach for compressible multi‐phase flows , 2008 .

[15]  Investigation of Convection and Pressure Treatment with Splitting Techniques , 1995 .

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

[17]  Keun-Shik Chang,et al.  Flux-Based Wave Decomposition Scheme for an Isentropic Hyperbolic Two-Fluid Model , 2011 .

[18]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[19]  N. U. Aydemir,et al.  Comparison of implicit and explicit AUSM‐family schemes for compressible multiphase flows , 2015 .

[20]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[21]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[22]  A. Debussche,et al.  A Density Perturbation Method to Study the Eigenstructure of Two-Phase Flow Equation Systems , 1998 .

[23]  Meng-Sing Liou,et al.  A New Approach to the Simulation of Compressible Multifluid Flows with AUSM+ Scheme , 2003 .

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

[25]  D. Bestion,et al.  Methodology, status and plans for development and assessment of Cathare code , 1997 .

[26]  Meng-Sing Liou,et al.  How to solve compressible multifluid equations: a simple, robust and accurate method , 2007 .

[27]  A. Harten.  High Resolution Schemes for Hyperbolic Conservation Laws , 2017 .

[28]  E. Shima,et al.  On New Simple Low-Dissipation Scheme of AUSM-Family for All Speeds , 2009 .

[29]  Bernd Einfeld.  On Godunov-type methods for gas dynamics , 1988 .

[30]  D. Drew,et al.  THE ANALYSIS OF VIRTUAL MASS EFFECTS IN TWO-PHASE FLOW , 1979 .

[31]  Steinar Evje,et al.  Weakly Implicit Numerical Schemes for a Two-Fluid Model , 2005, SIAM J. Sci. Comput..

[32]  M. S. Liou,et al.  Progress Towards and Improved CFD Method : AUSM+ , 1995 .

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

[34]  Meng-Sing Liou,et al.  An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities , 1997, SIAM J. Sci. Comput..

[35]  Meng-Sing Liou,et al.  A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM+-up scheme , 2007, J. Comput. Phys..

[36]  A. Kumbaro,et al.  An Approximate Linearized Riemann Solver for a Two-Fluid Model , 1996 .

[37]  Yang-Yao Niu,et al.  Advection upwinding splitting method to solve a compressible two‐fluid model , 2001 .

[38]  Charbel Farhat,et al.  A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosions , 2008, J. Comput. Phys..

[39]  J. Edwards,et al.  Low-Diffusion Flux-Splitting Methods for Flows at All Speeds , 1997 .

[40]  Meng-Sing Liou,et al.  A sequel to AUSM, Part II: AUSM+-up for all speeds , 2006, J. Comput. Phys..

[41]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[42]  I. Toumi,et al.  An upwind numerical method for two-fluid two-phase flow models , 1996 .