Numerical Simulations Using TVD Schemes of Two-Dimensional Supersonic Flow in Chemical Equilibrium

A numerical scheme for the solution of both unsteady and steady-state, two-dimensional Euler equations considering gas in chemical equilibrium, is presented. Three alternatives of the Total Variation Diminishing (TVD) Harten–Yee scheme are implemented. One of them is a technique based on the adaptive use of different limiter functions in each wave of the inter-cell Riemann problem. With this technique, the undesirable effects of the artificial viscosity on the capture of contact discontinuities are reduced, without loss of robustness in nonlinear waves resolution. In order to verify the accuracy of the proposed scheme, results of the unsteady flow in cylindrical explosions, and of the steady-state solution of hypersonic flow over a blunt body, are presented. Finally, comparisons considering accuracy of results and convergence properties between the three Harten–Yee schemes are carried out.

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

As compared to the two-fluid single-pressure model, the two-fluid seven-equation two-pressure model has been proved to be unconditionally well-posed in all situations, thus existing with a wide range of industrial applications. The classical 1st-order upwind scheme is widely used in existing nuclear system analysis codes such as RELAP5, CATHARE, and TRACE. However, the 1st-order upwind scheme possesses issues of serious numerical diffusion and high truncation error, thus giving rise to the challenge of accurately modeling many nuclear thermal-hydraulics problems such as long term transients. In this paper, a semi-implicit algorithm based on the finite volume method with staggered grids is developed to solve such advanced well-posed two-pressure model. To overcome the challenge from 1st-order upwind scheme, eight high-resolution total variation diminishing (TVD) schemes are implemented in such algorithm to improve spatial accuracy. Then the semi-implicit algorithm with high-resolution TVD schemes is validated on the water faucet test. The numerical results show that the high-resolution semi-implicit algorithm is robust in solving the two-pressure two-fluid two-phase flow model; Superbee scheme and Koren scheme give two highest levels of accuracy while Minmod scheme is the worst one among the eight TVD schemes.