Adaptive finite element method for thermal flow problems

This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems including heat transfer effects by forced or free convection. Conjugate heat transfer problems are also considered. Solutions are obtained in primitive variables by an Uzawa algorithm using a highly accurate finite element approximation on unstructured grids. Two error estimators are presented and compared on problems with known analytical solutions. The methodology is then applied to a problem of practical interest and predictions are compared with experimental measurements and show very good agreement.

[1]  O. Zienkiewicz,et al.  The hierarchical concept in finite element analysis , 1983 .

[2]  O. C. Zienkiewicz,et al.  Adaptive grid refinement for the Euler and compressible Navier-Stokes equations , 1984 .

[3]  K. S. Chen,et al.  Investigation of Natural Convection in Partially Divided Rectangular Enclosures Both With and Without an Opening in the Partition Plate: Measurement Results , 1990 .

[4]  Dominique Pelletier,et al.  Adaptive remeshing for convective heat transfer with variable fluid properties , 1994 .

[5]  D. Pelletier,et al.  Adaptive finite element method for turbulent flow near a propeller , 1994 .

[6]  O. C. Zienkiewicz,et al.  A simple error estimator and adaptive procedure for practical engineerng analysis , 1987 .

[7]  Michel Fortin,et al.  EXPERIMENTS WITH SEVERAL ELEMENTS FOR VISCOUS INCOMPRESSIBLE FLOWS , 1985 .

[8]  O. C. Zienkiewicz,et al.  Error estimation and adaptivity in Navier-Stokes incompressible flows , 1990 .

[9]  Dominique Pelletier,et al.  Adaptative remeshing for viscous incompressible flows , 1992 .

[10]  D. Pelletier,et al.  Adaptive finite element method for mixed convection , 1995 .

[11]  Dominique Pelletier,et al.  Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!) , 1989 .

[12]  Graham F. Carey,et al.  Adaptive grids for coupled viscous flow and transport , 1990 .

[13]  R. Verfürth.  A posteriori error estimators for the Stokes equations , 1989 .

[14]  Dominique Pelletier,et al.  Fast, Adaptive Finite Element Scheme for Viscous Incompressible Flows , 1992 .