Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

Kou, Jisheng; Sun, Shuyu

doi:10.1137/140969579

Cited by 27 publications

(23 citation statements)

References 40 publications

(46 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among these, engineering practice suggests that the geometric mean mixing rule is Downloaded 03/16/17 to 109.171.137.210. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php B7 most popularly adopted, that is, when β ij = 0 (see [16,21]). We apply this rule in the current manuscript.…”

Section: Bulk Properties Of Mixtures Modeled By the Peng-robinson Eosmentioning

confidence: 99%

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

Fan¹,

Kou²,

Qiao³

et al. 2017

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

Abstract. This paper presents a componentwise convex splitting scheme for numerical simulation of multicomponent two-phase fluid mixtures in a closed system at constant temperature, which is modeled by a diffuse interface model equipped with the Van der Waals and the Peng-Robinson equations of state (EoS). The Van der Waals EoS has a rigorous foundation in physics, while the Peng-Robinson EoS is more accurate for hydrocarbon mixtures. First, the phase field theory of thermodynamics and variational calculus are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic equations with extremely strong nonlinear source terms. The steady state equations are transformed into a transient system as a numerical strategy on which the scheme is based. The proposed numerical algorithm avoids the indefiniteness of the Hessian matrix arising from the second-order derivative of homogeneous contribution of total Helmholtz free energy; it is also very efficient. This scheme is unconditionally componentwise energy stable and naturally results in unconditional stability for the Van der Waals model. For the Peng-Robinson EoS, it is unconditionally stable through introducing a physics-preserving correction term, which is analogous to the attractive term in the Van der Waals EoS. An efficient numerical algorithm is provided to compute the coefficient in the correction term. Finally, some numerical examples are illustrated to verify the theoretical results and efficiency of the established algorithms. The numerical results match well with laboratory data.

show abstract

Section: Bulk Properties Of Mixtures Modeled By the Peng-robinson Eosmentioning

confidence: 99%

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

Fan¹,

Kou²,

Qiao³

et al. 2017

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Compared to the well-known Van der Waals equation of state, PR-EoS can provide more reasonable accuracy in predicting the properties of a wide variety of materials, such as N 2 , CO 2 and hydrocarbons. PR-EoS has been extensively applied for simulation of many important problems in petroleum and chemical engineering, for instance, phase equilibria calculations [7][8][9]13,[21][22][23]25] and prediction of surface tension between gas and liquid [7,10,11,24]. Modeling and simulation of compressible multi-component two-phase flows with partial miscibility and realistic equations of state (e.g.…”

mentioning

confidence: 99%

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Kou¹,

Sun²,

Wang³

2020

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

The Peng-Robinson equation of state (PR-EoS) has become one of the most extensively applied equations of state in chemical engineering and petroleum industry due to its excellent accuracy in predicting the thermodynamic properties of a wide variety of materials, especially hydrocarbons. Although great efforts have been made to construct efficient numerical methods for the diffuse interface models with PR-EoS, there is still not a linear numerical scheme that can be proved to preserve the original energy dissipation law. In order to pursue such a numerical scheme, we propose a novel energy factorization (EF) approach, which first factorizes an energy function into a product of several factors and then treats the factors using their properties to obtain the semiimplicit linear schemes. We apply the EF approach to deal with the Helmholtz free energy density determined by PR-EoS, and then propose a linear semi-implicit numerical scheme that inherits the original energy dissipation law. Moreover, the proposed scheme is proved to satisfy the maximum principle in both the time semi-discrete form and the cell-centered finite difference fully discrete form under certain conditions. Numerical results are presented to demonstrate the stability and efficiency of the proposed scheme.

show abstract

“…As a consequence, practical implementation of such schemes requires nonlinear iterative solvers and computational cost may be expensive accordingly. The other commonly used conventional approach for constructing linear numerical schemes is the linear stabilization approach [7,26,27,38,42,53,54], which simply treats all nonlinear terms by the fully explicit way and introduces a linear stabilization term to remove the time step constraint. We observe that the stabilization approach is effective for the double well potential, but it works not well for the logarithmic potential probably because of more complicate nonlinearity of it.…”

mentioning

confidence: 99%

Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential

2020

Self Cite

View full text Add to dashboard Cite

The Allen-Cahn equation is one of fundamental equations of phase-field models, while the logarithmic Flory-Huggins potential is one of the most useful energy potentials in various phasefield models. In this paper, we consider numerical schemes for solving the Allen-Cahn equation with logarithmic Flory-Huggins potential. The main challenge is how to design efficient numerical schemes that preserve the maximum principle and energy dissipation law due to the strong nonlinearity of the energy potential function. We propose a novel energy factorization approach with the stability technique, which is called stabilized energy factorization approach, to deal with the Flory-Huggins potential. One advantage of the proposed approach is that all nonlinear terms can be treated semiimplicitly and the resultant numerical scheme is purely linear and easy to implement. Moreover, the discrete maximum principle and unconditional energy stability of the proposed scheme are rigorously proved using the discrete variational principle. Numerical results are presented to demonstrate the stability and effectiveness of the proposed scheme.

show abstract

Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

Cited by 27 publications

References 40 publications

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State

A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Stabilized Energy Factorization Approach for Allen–Cahn Equation with Logarithmic Flory–Huggins Potential

Contact Info

Product

Resources

About