Chebyshev collocation method and multi-domain decomposition for Navier-Stokes equations in complex curved geometries

Journal Article · Tue Jun 01 04:00:00 EDT 1993 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1016/S0021-9991(83)71105-8· OSTI ID:5546187

Schneidesch, C R; Deville, M O ^[1]

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1. Universite Catholique de Louvain (Belgium)

A general multidomain decomposition is proposed for the numerical solution of the 2D incompressible stationary Navier-Stokes equations. The solution technique consists in a Chebyshev orthogonal collocation method preconditioned by a standard Galerkin finite element technique. The preconditioned system is then solved through a Richardson Procedure. The domain of interest is decomposed into quadrilaterals, curved when needed. A Gordon transfinite interpolation performs the curvilinear grid generation of the obtained simply-connected planar subdomains. The interface conditions, naturally incorporated into the finite element approach, relate neighbor subdomains through the normal jump of appropriate fluxes across internal boundaries, where an integral form of C[sup 1] continuity is consequently achieved at convergence of the iterative processes. The study of model Stokes problems demonstrates that the current method still behaves spectrally in distorted geometries. For curvilinear distortion, a loss of several orders of magnitude is observed in the solution accuracy even when the distortion is very limited. Finally, some results of flow Simulation in a constricted channel are proposed to illustrate the abilities of the present method to treat Navier-Stokes problems. 31 refs.

• OSTI ID: 5546187
• Journal Information: Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 106:2; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ACCURACY
ALGORITHMS
CALCULATION METHODS
COMPUTERIZED SIMULATION
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
GALERKIN-PETROV METHOD
ITERATIVE METHODS
MATHEMATICAL LOGIC
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
TWO-DIMENSIONAL CALCULATIONS