TY - JOUR
T1 - Extension of the fractional step method to general curvilinear coordinate systems
AU - Wu, Xiaohua
AU - Squires, Kyle D.
AU - Wang, Qunzhen
N1 - Funding Information:
Received 24 June 1994; accepted 24 August 1994. This work is supported by the Office of Naval Research (Grant N00014-94-1-0047, Program Officer: Dr. L. Patrick Purtell) and the National Institute of Occupational Safety and Health (Grant 0H03052-02). Computer time for the simulations was supplied by the Cornell Theory Center. Address correspondence to Kyle D. Squires, Department of Mechanical Engineering, University of Vermont, 209 Votey Building, Burlington, VT 05405, USA.
PY - 1995/3
Y1 - 1995/3
N2 - The extension of the fractional step method to three-dimensional, time-dependent incompressible flaws in non-orthogonal curvilinear coordinate systems is presented. A formulation based on block-LU decomposition is combined with a mixed implicit / explicit treatment of the discretized equations. Using local volume fluxes as dependent variables, the block-LU decomposition enables a unique definition of the sequential operations of the fractional step method for general coordinate systems. In this work a semi-direct scheme is developed for solution of the Poisson equation using series expansion along one coordinate direction that is discretized on a uniform, Cartesian grid. Also investigated in this study is solution of a simplified Poisson equation obtained by neglecting cross derivatives in the full Poisson equation. It is shown that for fractional step methods satisfaction of the zero-divergence constraint is still possible using the simplified Poisson equation, but the associated error is larger than θ(Δt).
AB - The extension of the fractional step method to three-dimensional, time-dependent incompressible flaws in non-orthogonal curvilinear coordinate systems is presented. A formulation based on block-LU decomposition is combined with a mixed implicit / explicit treatment of the discretized equations. Using local volume fluxes as dependent variables, the block-LU decomposition enables a unique definition of the sequential operations of the fractional step method for general coordinate systems. In this work a semi-direct scheme is developed for solution of the Poisson equation using series expansion along one coordinate direction that is discretized on a uniform, Cartesian grid. Also investigated in this study is solution of a simplified Poisson equation obtained by neglecting cross derivatives in the full Poisson equation. It is shown that for fractional step methods satisfaction of the zero-divergence constraint is still possible using the simplified Poisson equation, but the associated error is larger than θ(Δt).
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U2 - 10.1080/10407799508914952
DO - 10.1080/10407799508914952
M3 - Article
AN - SCOPUS:0029272316
SN - 1040-7790
VL - 27
SP - 175
EP - 194
JO - Numerical Heat Transfer, Part B: Fundamentals
JF - Numerical Heat Transfer, Part B: Fundamentals
IS - 2
ER -