Numerical Convection Algorithms and Their Role in Eulerian CFD Reactor Simulations

Abstract

In this paper a comparative convection algorithm study is presented. The performance of a large number of schemes is compared evaluating the predicted solutions for a standard benchmarking test problem. The nature of the errors caused by the numerical approximations to the convection term is highlighted. Although there is no algorithm that performs the best in general, several conclusions can be made. The tests performed show that the 1st order upwind scheme and several variations of this scheme are very diffusive and should be avoided. Most stable 2nd order schemes seem to be much more accurate, whereas the accuracy gained by higher order schemes (3rd order and 4th order) may be a little more costly. Implicit time integration schemes are usually not as efficient as the corresponding explicit schemes due to the computational time required on the iterative process. With larger time steps the accuracy of implicit schemes decrease rapidly. The choice of proper higher order schemes (2nd order schemes) is then seemingly determined by the trade-off between accuracy and computational time. The conservative methods like the UTOPIA, the QUICK-1D combined with a limiter, and a limited number of FCT and TVD formulations may be sufficient solving the multi-fluid model equations. For advective terms (e.g., as occur in the temperature equation) the non-flux-based modified method of characteristics is very fast, but also other higher order (2nd order) schemes performed well.