Comparison of Monolithic and Partitioned Approaches for the Solution of Fluid-Solid Thermal Interaction Problems

علوم کاربردی و محاسباتی در مکانیک

Article 3, Volume 31, Issue 1 - Serial Number 21, February 2020, Pages 23-38   

Document Type: Original Article

DOI: 10.22067/fum-mech.v31i1.84760

Author

Ali Ashrafizadeh

K. N. Toosi University of Technology

Abstract

Numerical solution of conjugate heat transfer (CHT) problems in multi-region domains is a challenging issue in terms of efficiency and stability due to inherent coupling between governing equations in separate sub-domains. This paper aims at comparing two distinct strategies for coupling energy equations at interface of regions: partitioned and monolithic. While the former enforces strong coupling via iterative procedures, the latter suggests simultaneous solution of energy equation throughout all regions at once. More precisely, the primary objective of this study is to compare computational costs for three finite volume- based CHT solvers which share a same method for handling pressure-velocity coupling in the fluid, i.e. semi-implicit projection method, and are distinguished from the coupling strategy for energy equation at interface of interacting sub-domains. The first method applies simultaneous solution of energy equation across all regions while second and third ones use separate solver for each region with difference in handling iterative loops. The accuracy and convergence rate of three algorithms are assessed via transient solution of conjugate free convection in fluid and conduction in vertical wall. Finally, it is concluded that, in contrast to partitioned solver in OpenFOAM for CHT problems, employing a separate loop to enforce energy-energy coupling per iteration, can be much more beneficial in terms of computational costs.

Keywords

Conjugate heat transfer; Monolithic; Partitioned; Coupling; Finite Volume; Convergence Rate; OpenFOAM

Supplementary Files

EA3-tandis-Nahayi.pdf

References

1. Pozzi, A. and Tognaccini, R., "Time singularities in conjugated thermo-fluid-dynamic phenomena", Journal of Fluid Mechanics,Vol. 538, pp. 361-376, (2005).

2. Pozzi, A. and Tognaccini, R., "Coupling of conduction and convection past an impulsively started semi-infinite flat plate", International journal of heat and mass transfer, Vol. 43, pp. 1121-1131, (2000).

3. Fourcher, B. and Mansouri, K., "An approximate analytical solution to the Graetz problem with periodic inlet temperature", International journal of heat and fluid flow, Vol. 18, pp. 229-235, (1997).

4. Ismail, K. and Henriquez, J., "Two-dimensional model for the double glass naturally ventilated window", International Journal of Heat and Mass Transfer, Vol. 48, pp. 461-475, (2005).

5. Gunes, H., "Low-order dynamical models of thermal convection in high-aspect ratio enclosures", Fluid dynamics research, Vol. 30, pp. 1-30, (2002).

6. Park, S. and Lee, C., "Analysis of coherent structures in Rayleigh–Benard convection", Journal of Turbulence, Vol. 16, pp. 1162-1178, (2015).

7. Moretti, R., Errera, M.-P., Couaillier, V. and Feyel, F., "Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction", International Journal of Thermal Sciences, Vol. 126, pp. 23-37, (2018).

8. Felippa, C. and Park, K., "Staggered transient analysis procedures for coupled mechanical systems: formulation", Computer Methods in Applied Mechanics and Engineering, Vol. 24, pp. 61-111, (1980).

9. Le Tallec, P., "Domain decomposition methods in computational mechanics", Computational mechanics advances, Vol. 1, pp. 121-220, (1994).

10. Piperno, S., Farhat, C. and Larrouturou, B., "Partitioned procedures for the transient solution of coupled aroelastic problems Part I: Model problem, theory and two-dimensional application", Computer methods in applied mechanics and engineering, Vol. 124, pp. 79-112, (1995).

11. Pan, X., Kim, K., Lee, C. and Choi, J.-I., "A decoupled monolithic projection method for natural convection problems", Journal of Computational Physics, Vol. 314, pp. 160-166, (2016).

12. Pan, X., Lee, C. and Choi, J.-I., "Efficient monolithic projection method for time-dependent conjugate heat transfer problems", Journal of Computational Physics, Vol. 369, pp. 191-208, (2018).

13. Radenac, E., Gressier, J. and Millan, P., "Methodology of numerical coupling for transient conjugate heat transfer", Computers & Fluids, Vol. 100, pp. 95-107, (2014).

14. Meng, F., Banks, J.W., Henshaw, W.D. and Schwendeman, D.W., "A stable and accurate partitioned algorithm for conjugate heat transfer", Journal of Computational Physics, Vol. 344, pp. 51-85, (2017).

15. Errera, M.-P. and Duchaine, F., "Comparative study of coupling coefficients in dirichlet–robin procedure for fluid–structure aerothermal simulations", Journal of Computational Physics, Vol. 312, pp. 218-234, (2016).

16. Scholl, S., Janssens, B. and Verstraete, T., "Stability of static conjugate heat transfer coupling approaches using Robin interface conditions", Computers & Fluids, Vol. 172, pp. 209-225, (2018).

17. Versteeg, H.K. and Malalasekera, W., "An introduction to computational fluid dynamics: the finite volume method", Pearson education, (2007).

18. van der Heul, D.R., Vuik, C. and Wesseling, P., "A conservative pressure-correction method for flow at all speeds", Computers & Fluids, Vol. 32, pp. 1113-1132, (2003).

19. Uroić, T. and Jasak, H., "Block-selective algebraic multigrid for implicitly coupled pressure-velocity system", Computers & fluids, Vol. 167, pp. 100-110, (2018).

20. Jasak, H., Jemcov, A. and Tukovic, Z., "OpenFOAM: A C++ library for complex physics simulations, International workshop on coupled methods in numerical dynamics", IUC Dubrovnik Croatia, pp. 1-20, (2007).

21. Konle, M., AG, M.A.E., de Guillebon, L. and Cottier, F., "Multi-Physics Simulations of an Aero Engine Combustor with OpenFoam", Proceedings of 1st Global Power and Propulsion Forum, GPPF-2017-0045, Zurich, (2017).

22. el Abbassia, M., Lahaye, D. and Vuik, C., "Modelling turbulent combustion coupled with conjugate heat transfer in openfoam", Conference: Tenth Mediterranean Combustion Symposium, (2017)

23. Issa, R.I., "Solution of the implicitly discretised fluid flow equations by operator-splitting", Journal of computational physics, Vol. 62, pp.40-65, (1986).

24. Kazemi‐Kamyab, V., Van Zuijlen, A. and Bijl, H., "Accuracy and stability analysis of a second‐order time‐accurate loosely coupled partitioned algorithm for transient conjugate heat transfer problems", International Journal for Numerical Methods in Fluids, Vol. 74, pp. 113-133, (2014).

25. Kazemi-Kamyab, V., Van Zuijlen, A. and Bijl, H., "Analysis and application of high order implicit Runge–Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach", Journal of Computational Physics, Vol. 272, pp. 471-486, (2014).