An assessment of using the predictor–corrector technique to solve reactive transport equations

Cheng, Hsu-Tang; Li, Ming Hsu; Cheng, Jing

doi:10.1002/nme.586

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…The proposed iterative scheme solves the upgraded non-linear convection-diffusion model between a predictor and a corrector phase (Goldschmit and Cavaliere, 1997;Cheng et al, 2003), taking into account the addition of thermodynamic relations. The heat of vaporization is included.…”

Section: Predictor-corrector Iterative Schemementioning

confidence: 99%

Thermal‐fluid flow within innovative heat storage concrete systems for solar power plants

Salomoni

Majorana

Giannuzzi

et al. 2008

Int Jnl of Num Meth for HFF

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Purpose -The purpose of this paper is to describe an experience of R&D in the field of new technologies for solar energy exploitation within the Italian context. Concentrated solar power systems operating in the field of medium temperatures are the main research objectives, directed towards the development of a new and low-cost technology to concentrate the direct radiation and efficiently convert solar energy into high-temperature heat. Design/methodology/approach -A multi-tank sensible-heat storage system is proposed for storing thermal energy, with a two-tanks molten salt system. In the present paper, the typology of a below-grade cone shape storage is taken up, in combination with nitrate molten salts at 5658C maximum temperature, using an innovative high-performance concrete for structures absolving functions of containment and foundation. Findings -Concrete durability in terms of prolonged thermal loads is assessed. The interaction between the hot tank and the surrounding environment (ground) is considered. The developed FE model simulates the whole domain, and a fixed heat source of 1008C is assigned to the internal concrete surface. The development of the thermal and hygral fronts within the tank thickness are analysed and results discussed for long-term scenarios. Originality/value -Within the medium temperature field, an innovative approach is here presented for the conceptual design of liquid salts concrete storage systems. The adopted numerical model accounts for the strong coupling among moisture and heat transfer and the mechanical field. The basic mathematical model is a single fluid phase non-linear diffusion one based on the theory by Bažant; appropriate thermodynamic and constitutive relationships are supplemented to enhance the approach and catch the effects of different fluid phases (liquid plus gas).

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Section: Predictor-corrector Iterative Schemementioning

confidence: 99%

Thermal‐fluid flow within innovative heat storage concrete systems for solar power plants

Salomoni

Majorana

Giannuzzi

et al. 2008

Int Jnl of Num Meth for HFF

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“…Although operator-splitting methods are easy to implement and require less computational capability, they introduce operator-splitting error into the simulated results (Valocchi and Malmstead 1992;Lu et al 1996; Barry et al 1996aBarry et al , 1996bBarry et al , 2000Cheng et al 2003;Hammond et al 2004). Several investigators have analyzed the splitting error to advectiondispersion-reaction simulations (Valocchi and Malmstead 1992;Kaluarachchi and Morshed 1995;Morshed and Kaluarachchi 1995;Barry et al 1996aBarry et al , 1996bBarry et al , 2000Lanser and Verwer 1999;Carrayrou et al 2004).…”

Section: Introductionmentioning

confidence: 97%

Modeling reactive transport using exact solutions for first-order reaction networks

Sun

Buscheck

2007

Transp Porous Med

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Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational efficiency and simulation accuracy.

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“…The former would require much more refined grid to capture the flow field detail, and the latter would increases the number of species transport equations in each grid node and produces very stiff chemical source term in species transport and energy conservation equations. As a result, the main difficult encountered in numerical simulation of the combustion systems is that the Navier-Stokes equations extended to chemical reaction flow, containing stiff chemical reaction source, would be solved in an acceptable memory and computation time [1].…”

Section: Introductionmentioning

confidence: 99%

A Modified Implicit Iterative Difference Algorithm for Stiff Chemical Kinetic Equations in Complex Combustion System

Nie

Feng

et al. 2011

AMR

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The splitting-operator method has been widely used in the numerical simulation of complex combustion system with its high computation efficiency. The main difficult encountered in the method is how to integrate the stiff chemical kinetics ordinary differential equation (ODE) efficiently and accurately in each grid node of flow field. Although several ODE software packages such as LSODE and VODE have very predominant performance in integrating stiff and non-stiff case, it couldn’t ensure the positivity of mass fraction in integrating stiff chemical kinetic ODE. A detail liquid rocket hypergolic bipropellant combination of Monomethylhydrazine (MMH)/Red Fuming Nitric Acid (RFNA) chemical mechanism consisting of 550 elementary reactions among 83 species was constituted basing on several relevant literatures firstly. And then a modified implicit iterative difference algorithm with variable time steps was developed to tackle the problem of mass fraction non-positive. The results from the integration of MMH /nitrogen tetroxide (NTO) chemical kinetic ODE indicate that the algorithm is always retain stability and positive value of mass fraction. The time step length would also be automatically adjusted at different chemical reaction time in the algorithm to keep its computational efficiency.

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An assessment of using the predictor–corrector technique to solve reactive transport equations

Cited by 4 publications

References 29 publications

Thermal‐fluid flow within innovative heat storage concrete systems for solar power plants

Thermal‐fluid flow within innovative heat storage concrete systems for solar power plants

Modeling reactive transport using exact solutions for first-order reaction networks

A Modified Implicit Iterative Difference Algorithm for Stiff Chemical Kinetic Equations in Complex Combustion System

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