Summary
A scheme for computing 3D unsteady flow with large temperature difference is presented. The compressible Navier-Stokes equations are approximated, assuming that the density variation due to pressure difference is small, so that the effect of the acoustic wave propagation, which is not of primary importance in low Mach-number flows, is removed. In this scheme, linear systems which result from the discretization of the pressure equation are large, sparse, nonsymmetric and, in addition, not diagonally dominant. In this study, a preconditioned conjugate gradient (PCG) method suited to vectorsupercomputers is applied for solving these stiff linear systems. Numerical experiments are done to investigate the thermal convection in the chemical vapor deposition reactor used for the manufacture of electronic devices. Results show the effect of unsteady buoyant flow caused by a large temperature difference. The efficiency of the PCG linear solver on vectorsupercomputers is also demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jansen, N., Orazem, M. E., Fox, B. A. and Jesser, W. A.:“Numerical study of the influence of reactor design on MOCVD with a comparison to experimental data”, J. Cryst. Growth, Vol. 112 (1991), pp. 316–336.
Harlow, F. H. and Welch, J. E.:“Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface”, Phys. Fluids, Vol. 8 (1965), pp. 2182–2189.
Chorin, A. J.:“Numerical Solution of the Navier-Stokes Equations”, Math. Comput., Vol. 22 (1968), pp. 745–762.
Kuwahara, K.:“Computation of Thermal Convection with a Large Temperature Difference”, Proc. of 4th Int. Conf. on Appl. Num. Modeling (1984).
Fletcher, R.:“Conjugate Gradient Method for Indefinite Systems”, Lecture Notes in Mathematics 506, pp. 73–89, Springer-Verlag (1976).
Doi, S. and Harada, N.:“Tridiagonal Factorization Algorithm: A Preconditioner for Nonsymmetric System Solving on Vectorcomputers”, J. Info. Process., Vol. 11 (1988), pp. 138–146.
Kawamura, T. and Kuwahara, K.:“Computation of High Reynolds Number Flow around a Circular Cylinder with Surface Roughness”, AIAA paper 84–0340 (1984).
Van der Vorst, H. A.:“Iterative Solution Methods for Certain Sparse Linear Systems with a Non-Symmetric Matrix Arising from PDE-Problems”, J. Compt. Phys., Vol. 44 (1981), pp. 1–19.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Fachmedien Wiesbaden
About this paper
Cite this paper
Akiba, Y., Doi, S., Kuwahara, K. (1992). Analysis of Natural Convection with Large Temperature Difference Using a Fast Matrix Solver. In: Vos, J.B., Rizzi, A., Ryhming, I.L. (eds) Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 35. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13974-4_32
Download citation
DOI: https://doi.org/10.1007/978-3-663-13974-4_32
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07635-1
Online ISBN: 978-3-663-13974-4
eBook Packages: Springer Book Archive