Phase appearance or disappearance in two-phase flows

This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. After an asymptotic study of the model, this paper proposes accurate and robust numerical methods adapted to the simulation of phase appearance or disappearance. Polynomial solvers are developed to avoid the use of eigenvectors which are needed in usual shock capturing schemes, and a method based on an adaptive numerical diffusion is designed to treat the positivity problems. An alternate method, based on the use of the hyperbolic tangent function instead of a polynomial, is also considered. Numerical results are presented which demonstrate the efficiency of the proposed solutions

Scaling of the Steady-State Load Flow Equations for Multi-Carrier Energy Systems

Coupling single-carrier networks (SCNs) into multi-carrier energy systems (MESs) has recently become more important. Steady-state load flow analysis of energy systems leads to a system of nonlinear equations, which is usually solved using the Newton-Raphson method (NR). Due to various physical scales within a SCN, and between different SCNs in a MES, scaling might be needed to solve the nonlinear system. In single-carrier electrical networks, per unit scaling is commonly used. However, in the gas and heat networks, various ways of scaling or no scaling are used. This paper presents a per unit system and matrix scaling for load flow models for a MES consisting of gas, electricity, and heat. The effect of scaling on NR is analyzed. A small example MES is used to demonstrate the two scaling methods. This paper shows that the per unit system and matrix scaling are equivalent, assuming infinite precision. In finite precision, the example shows that the NR iterations are slightly different for the two scaling methods. For this example, both scaling methods show the same convergence behavior of NR in finite precision.</p

Shape Sensitivity of Free-Surface Interfaces Using a Level Set Methodology

In this paper we develop the continuous adjoint methodology to compute shape sensitivities in free-surface hydrodynamic design problems using the incompressible Euler equations and the level set methodology. The identification of the free-surface requires the convection of the level set variable and, in this work, this equation is introduced in the entire shape design methodology. On the other hand, an alternative continuous adjoint formulation based in the jump condition across the interface, and an internal adjoint boundary condition is also presented. It is important to highlight that this new methodology will allow the specific design of the free-surface interface, which has a great potential in problems where the target is to reduce the wave energy (ship design), or increase the size of the wave (surfing wave pools). The complete continuous adjoint derivation, the description of the numerical methods (including a new high order numerical centered scheme), and numerical tests are detailed in this paper. I