Analysis and application of high order implicit Runge–Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach

Kazemi-Kamyab, V.; Zuijlen, A.H. van; Bijl, H.

doi:10.1016/j.jcp.2014.04.016

Cited by 28 publications

(8 citation statements)

References 27 publications

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“…Nowadays, there has been great progress in the development of advanced mathematical models as well as physical applications; see, for instance, [10,[21][22][23][24][25][26][27][28][29][30][31][32][33] and the references therein. In the case of mathematical analysis, the works are focused on topics like the local existence of solutions, the global existence of solutions, the well-posedness of the mathematical models, the asymptotic behavior of the solutions, energy decay, the numerical solutions, and the convergence of the numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Coronel,

Lozada,

Berres

et al. 2024

Energies

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In this article, we propose a mathematical model for one-dimensional heat conduction in a three-layered solid considering that an interfacial condition is present for the temperature and heat flux conditions between the layers. The numerical approach is developed by constructing a finite difference scheme to solve the initial boundary–interface problem. The numerical scheme is designed by considering the accuracy of the model on the inner part of each layer, then extending to the interfaces and boundaries by incorporating the continuous interfacial conditions. The finite difference scheme is unconditionally stable, convergent, and easy to implement since it consists of the solution of two algebraic systems. We provide three numerical examples to confirm that our numerical approximation is consistent with the analytical solution and the physical phenomenon.

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Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Coronel,

Lozada,

Berres

et al. 2024

Energies

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“…The study of transfer heat problems between different substances, for instance, solids of different types or solids and fluids, are considered by several researchers [15][16][17][18][19][20][21][22][23]. The motivations are of different types: simple examples, analytical solutions, creation of mathematical models, different applications, theoretical study, and numerical simulations [15].…”

Section: Introductionmentioning

confidence: 99%

“…The motivations are of different types: simple examples, analytical solutions, creation of mathematical models, different applications, theoretical study, and numerical simulations [15]. Particularly, in relation to the numerical solutions, we propose several numerical methods including the use of high-order implicit time integration schemes [17], hybrid boundary element method and radial basis integral equation [18], high-order finite volume schemed [19], projection method [20], high-order implicit Runge-Kutta schemes [21], and finite difference methods [23].…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Coronel

Huancas

Lozada

et al. 2022

Axioms

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In this article, we propose a one-dimensional heat conduction model for a double-pane window with a temperature-jump boundary condition and a thermal lagging interfacial effect condition between layers. We construct a second-order accurate finite difference scheme to solve the heat conduction problem. The designed scheme is mainly based on approximations satisfying the facts that all inner grid points has second-order temporal and spatial truncation errors, while at the boundary points and at inter-facial points has second-order temporal truncation error and first-order spatial truncation error, respectively. We prove that the finite difference scheme introduced is unconditionally stable, convergent, and has a rate of convergence two in space and time for the L∞-norm. Moreover, we give a numerical example to confirm our theoretical results.

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“…Therefore, researchers have developed solutions with different calculation efficiency and accuracy for different problems. The transient tight coupling method can get effective results, but it consumes a lot of computing resources and is difficult to solve practical complex engineering problems [19][20][21]. The loose coupling method based on the quasi-steady flow field considers that in the whole process of fluid-solid coupling heat transfer, the flow field is in several quasi-steady states, and each quasi-steady flow field is solved by the steady-state Navier-Stokes equations; the research results show that the algorithm can greatly improve the calculation efficiency, but the deviation of the calculation results is large, which is mainly due to the large deviation between the treatment method of completely isolating the flow field from other parts and the actual coupling relationship [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Study on Heat Exchange Structure Design and Propulsion Performance of Solar Thermal Thruster

Zhang

Huang

2022

International Journal of Aerospace Engineering

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This paper designed a platelet heat exchanger in the solar thermal thruster and analyzed the unsteady-state conjugate heat transfer characteristics between heat exchanger and propellant. The conjugate heat transfer (CHT) computational fluid dynamics (CFD) simulation of the 3D model of the platelet under steady-state conditions was carried out with different mass flow rates to find the empirical correlation between the average Nusselt number and the average Reynolds number. The unsteady-state 1D simplified model of the heat exchanger was established using a loose coupling algorithm based on quasi-steady flow domain and finally verified by experiments. The results show that the platelet structure could heat the working medium to more than 2380 K with the heat transfer efficiency of 87% and produce a peak thrust of 0.57 N and specific impulse of 2200 m/s; in steady state, the outlet temperature and heat transfer efficiency of the heat exchanger were stable at 1950 K and 69%. Moreover, 1D model could accurately reflect the real heat exchange situation to a certain extent, the simulation error was less than 5% compared with the 3D model, and the calculation time was greatly shortened, making it more convenient to adjust the heat exchange strategy. The experimental results were consistent with the simulation results at the initial stage of heat exchange, and the difference was mainly reflected in the steady-state stage, which might be caused by the lack of precision of the experimental equipment.

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Analysis and application of high order implicit Runge–Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach

Cited by 28 publications

References 27 publications

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

Mathematical Modeling and Numerical Approximation of Heat Conduction in Three-Phase-Lag Solid

A Numerical Method for a Heat Conduction Model in a Double-Pane Window

Study on Heat Exchange Structure Design and Propulsion Performance of Solar Thermal Thruster

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