Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation

TL;DR

This paper investigates the multiple solutions of the NCCR model for non-equilibrium flows, proposes a new numerical method to identify the physical solution, and validates it through flow simulations across various regimes.

Contribution

A novel numerical approach converts NCCR equations into a single-variable optimization problem, enabling identification of the physical solution and improving solution stability.

Findings

Multiple solutions of NCCR are identified and characterized.

The proposed method effectively isolates the physical solution.

Validation shows improved accuracy in flow simulations across regimes.

Abstract

In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are firstly observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the generalized hydrodynamic equations of Eu, and aims to describe rarefied flows. The NCCR model is a complicated nonlinear system. Many assumptions have been used in the schemes for solving the NCCR equations. The corresponding numerical methods may be associated with unphysical solution and instability. At the same time, it is hard to analyze the physical accuracy and stability of NCCR model due to the uncertainties in the numerical discretization. In this study, a new numerical method for solving NCCR equations is proposed and used to analyze the properties of NCCR equations. More specifically, the nonlinear equations are converted into the solutions of an objective function of a single variable. Under this formulation, the multiple solutions of the NCCR system are identified and the criteria for picking up the physical solution are proposed. Therefore, a numerical scheme for solving NCCR equations is constructed. A series of flow problems in the near continuum and low transition regimes with a large variation of Mach numbers are conducted to validate the numerical performance of proposed method and the physical accuracy of NCCR model.