Phase appearance or disappearance in two-phase flows

TL;DR

This paper addresses numerical challenges in simulating two-phase flows during phase appearance or disappearance, proposing robust methods to handle loss of hyperbolicity and positivity issues, with demonstrated effectiveness in simulations.

Contribution

It introduces novel numerical schemes that avoid eigenvector computations and ensure positivity, improving the robustness of two-phase flow simulations during phase transitions.

Findings

Proposed polynomial solvers eliminate the need for eigenvector calculations.

Adaptive numerical diffusion effectively maintains positivity.

Numerical results confirm the efficiency of the new methods.

Abstract

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.