×

A nodal coarse-mesh method for the efficient numerical solution of laminar flow problems. (English) Zbl 0579.65130

Summary: A coarse-mesh nodal method for the efficient numerical solution of incompressible laminar flow problems is developed using a transverse integration procedure followed by the introduction of locally-defined Green’s tensors of the transverse-integrated in-node Navier-Stokes and mass conservation equations. In applications to two-dimensional flow problems, including fully developed flow, inlet flow, and modified driven cavity problems (driven cavities with inlet and outlet sections), this new nodal Green’s tensor method is demonstrated to have very high accuracy even when applied on very large nodes. The high accuracy of this new method on very coarse meshes leads to a high computational efficiency (reduced computer time for fixed accuracy requirements).

MSC:

65Z05 Applications to the sciences
76D05 Navier-Stokes equations for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
35Q30 Navier-Stokes equations

Software:

NACHOS; SOLA
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Richtmeyer, R. D.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[2] Nakamura, S., Computational Methods in Engineering and Science (1977), Interscience: Interscience New York
[3] Roache, P. J., Computational Fluid Dynamics (1976), Hermosa: Hermosa Albuquerque, N. M
[4] Dorodnitsyn, A. A., Review of methods for solving the Navier-Stokes equations, (Proceedings Int. Conf. on Numerical Methos in Fluid Mechanics (1973)), No. 1 · Zbl 0257.76019
[5] Lomax, H., AIAA J., 14, 512 (1976)
[6] Hirt, C. W.; Nichols, B. D.; Romero, N. C., SOLA-A Numerical Solution Algorithm for Transient Fluid Flows, LA-5852 (1975)
[7] Hornbeck, R. W., Numerical Marching Techniques for Fluid Flows with Heat Transfer, NASA SP-297 (1973) · Zbl 0265.76042
[8] Zienkiewicz, O. C., The Finite Element Method in Structural and Continuum Mechanics (1971), McGraw-Hill: McGraw-Hill New York · Zbl 0237.73071
[9] Martin, H. C.; Carey, G. F., Introduction to—Finite Element Analysis (1973), McGraw-Hill: McGraw-Hill New York
[10] Baker, A. J., Int. J. Numer. Methods Eng., 6, 89 (1973)
[11] Taylor, C.; Hood, P., Comput. Fluids, 1, 73 (1973)
[12] Smith, S. L.; Brebbia, C. A., J. Comput. Phys., 17, 235 (1975)
[13] Lynn, P. P.; Alani, K., Int. J. Numer. Methods Eng., 10, 809 (1976)
[14] Oden, J. T.; Wellford, L. C., AIAA J., 1590 (1972)
[15] Gartling, D. K., NACHOS: A Finite Element Computer Program for Incompressible Fluid Flow Problems, Part. 1: Theoretical Background, SAND-77-1333 (1978)
[16] Gartling, D. K., NACHOS: A Finite Element Computer Program for Incompressible Fluid Flow Problems, Part 2: User’s Manual, SAND-77-1334 (1977)
[17] Connor, J. J.; Brebbia, C. A., Finite Element Techniques for Fluid Flow (1976), Newnes: Newnes London · Zbl 0431.76001
[18] Gray, W. H.; Schnurr, N. M., Comput. Methods Appl. Mech. Eng., 6, 243 (1975) · Zbl 0306.65074
[19] Gray, W. H.; Pinder, G. F., Int. J. Numer. Methods Eng., 10, 893 (1976)
[20] Langenbuch, S.; Maurer, W.; Werner, W., Nucl. Sci. Eng., 64, 508 (1977)
[21] Romstedt, P.; Werner, W., Nucl. Sci. Eng., 64, 208 (1977)
[22] Werner, W., Higher order methods in fluid dynamics, (Computational Methods in Nuclear Engineering. Computational Methods in Nuclear Engineering, Williamsburg topical meeting, Vol. 1 (1979)), 1
[23] Graf, U.; Werner, W., Application of the ASWR method to 3D two-phase flow problems, (Computational Methods in Nuclear Engineering. Computational Methods in Nuclear Engineering, Williamsburg topical meeting, Vol. 3 (1979)), 10-27
[24] Hess, J. L., Comput. Methods Appl. Mech. Eng., 5, 145 (1975)
[25] Brebbia, C. A., Fundamentals of boundary elements, (Brebbia, C. A., New Developments in Boundary Element Methods (1980), CML Publ: CML Publ Southampton, U. K), 3 · Zbl 0458.73080
[26] Burns, T. J.; Dorning, J. J., The partial current balance method: A new computational method for the solution of multi-dimensional neutron diffusion problems, (Proceedings of the Joint NEACRP/CSNI Specialists’ Meeting in New Developments in Three-Dimensional Neutron Kinetics and Benchmark Calculations (1975), Laboratorium fur Reaktorregelung and Anlagensicherung: Laboratorium fur Reaktorregelung and Anlagensicherung Garching, Munich, Germany), 109, See also
[27] Lawrence, R. D.; Dorning, J. J., Nucl. Sci. Eng., 76, 218 (1980), See also
[28] Horak, W. C.; Dorning, J. J., Nucl. Sci. Eng., 64, 192 (1977)
[29] Horak, W. C.; Dorning, J. J., A coarse-mesh method for heat flow analysis based upon the use of locally-defined Green’s functions, (Lewis, R. W.; Morgan, K.; Schrefler, B. A., Num. Meth. in Thermal Problems, 2 (1981), Pineridge: Pineridge Swansea, U.K), 515
[30] Schlichting, H., Boundary Layer Theory (1968), McGraw-Hill: McGraw-Hill New York
[31] Horak, W. C.; Dorning, J. J., A nodal Green’s tensor method for the efficient numerical solution of laminar flow problems, (Taylor, C.; Schrefler, B. A., Num. Meth. in Laminar and Turbulent Flow (1981), Pineridge: Pineridge Swansea, U.K), 103 · Zbl 0486.76050
[32] Tuann, Shih-Yu; Olson, Mervyn D., J. Comput. Phys., 29, 1 (1978)
[33] Horak, W. C.; Dorning, J. J., Trans. Amer. Nucl. Soc., 30, 215 (1978)
[34] Horak, W. C., Local Green’s Function Techniques for the Solution of Heat Conduction and Incompressible Fluid Flow Problems, (Ph.D. thesis (1980), Univ. of Illinois: Univ. of Illinois Urbana)
[35] Patankar, S. V., Numerical Heat Transfer and Fluid Flow (1980), McGraw-Hill: McGraw-Hill New York · Zbl 0595.76001
[36] Beernick, K. P.; Dorning, J. J., The relationships between the nodal, and moments characteristic, transport methods and their errors, Advances in Reactor Computations, 737 (1984), Salt Lake City
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.