No abstract

We analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. In order to achieve unconditional monotonicity, hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy, while keeping the native L-stability property, which is useful for the application to stiff problems. Numerical experiments compare these different hybridization strategies to other methods used in stiff and mildly stiff problems. The results show that the proposed strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in literature

We propose an efficient, accurate, and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a number of classical benchmarks, which highlight its superior efficiency with respect to other widely used implicit approaches. The parallel implementation of the proposed method in the framework of the deal.II software package allows for accurate and efficient adaptive simulations in complex geometries, which makes the proposed solver attractive for large scale industrial applications.

Abstract. The first aim of this work is to improve the models currently available for the simulation of ice production in turbulent seawater, by means of the development of a multiphase model able to describe all the stages of ice production, overcoming the limitation of previous attempts, mainly based on Boussinesq approximation. We consider the mixture of ice and seawater as a dense compressible fluid, and we model the behaviour of seawater by an equation of state that links seawater density to temperature, salinity and pressure. The model is able to reproduce the interaction phenomena occurring between phases when the ice volume fraction exceeds the values allowed by the Boussinesq approximation, including in the momentum equations additional terms, related to the drag force between liquid and particles, and to the particle-particle interaction force. The second aim of our work is to implement and validate a numerical solver of our model. For this purpose, the model uses a sophisticated modelling approach, typically adopted for the numerical simulation of multiphase flows of industrial interest. The multiphase model can be coupled to the Large Eddy Simulation technique. The behaviour of the governing equations in the incompressible limit is investigated by means of a low-Mach number asymptotic analysis. The divergence constraint condition for the velocity field of continuous phase can then been imposed on the zero-Mach number equations by means of a projection method. The governing equations are discretized using the finite volume method, and the performance of the multiphase model has been assessed by solving a laminar Rayleigh-Bénard convection, for both large and small ice concentration regimes. In small concentration regime, the numerical solutions have been compared with the solutions obtained by a finite difference numerical code, based on the Boussinesq approximation.

The European Green Deal, the Paris COP21 agreement, the EU roadmap for a competitive low-carbon economy in 2050 and more recently the “Fit for 55” package set the targets of greenhouse gas (GHG) emissions for several sectors. In this context, hydrogen will be relevant as a feedstock, fuel and energy storage solution. Today hydrogen use in steel industry is limited to annealing processes on a small quantity, therefore a complete transformation of the steelmaking production route from liquid steel process (Upstream) up to the rolling and finishing line (Downstream) requires development and validation of new technologies. The massive usage of hydrogen in steel industry is envisioned in the Carbon Direct Avoidance pathway reported in the Strategic Research Agenda (SRA) of the Private Public Partnership Clean Steel. The paper presents the Tenova SmartBurner technology: TSX recuperative flameless for reheating applications ready to use hydrogen as fuel (up to 100%), with nitric oxides reached in the operative range from 100% natural gas to 100% hydrogen – well below the next envisioned limits (80 mg/Nm3 at 5% of O2 with furnace at 1250 °C).