which is based upon a semi-implicit finite difference method with staggered grid and donor-cell discretization A second-order accurate scheme based on high-resolution shockcapturing methods was used with a typical two-phase flow model of the convective terms [35]. The main advantages of such which is used in the computer codes for simulation of nuclear power a scheme are robustness and efficiency. The weak side of plant accidents. The two-fluid model, which has been taken from the the scheme is its numerical dissipation, which tends to computer code RELAP5, consists of six first-order partial differential smear discontinuities on coarse grids. Numerical dissipaequations that represent 1D mass, momentum, and energy balances tion cannot be easily avoided with the existing type of the for vapour and liquid. The partial differential equations are illposed-nonhyperbolic. The hyperbolicity required by the presented scheme, since this dissipation presents the main mechanism numerical scheme was obtained in the practical range of the physiwhich removes the ill-posedness from the discretized equacal parameters by minor modification of the virtual mass term. No tions and ensures the scheme's stability. The RELAP5 conservative form of the applied equations exists, therefore, instead code successfully covers the area of the transients with of the Riemann solver, more basic averaging was used for the characteristic time scale determined by the fluid velocity evaluation of the Jacobian matrix. The equations were solved using nonconservative and conservative basic variables. Since the source [27], but it has to be used with extreme caution for tranterms are stiff, they were integrated with time steps which were sients with acoustic waves [21].
shorter than or equal to the convection time step. The sources were
The main directions of the development of today's twotreated with Strang splitting to retain the second-order accuracy phase flow models are: improvement of the mathematical of the scheme. The numerical scheme has been used for the models (better closure models, from 1D into 3D) and imsimulations of the two-phase shock tube problem and the Edwards pipe experiment. Results show the importance of the closure laws provement of the numerical methods. To obtain optimum which have a crucial impact on the accuracy of two-fluid models.
results, parallel improvement in both fields is necessary. Advantages of the second-order accurate schemes are evident This paper presents the application of an advanced numeriespecially in the area of fast transients dominated by acoustic cal scheme using the existing two-fluid model of RELAP5 phenomena. แฎ 1997 Academic Press computer code; however, we believe that this type of numerical schemes will also be useful for the next generation of mathematical models of two-phase flow.
503