Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

Journal Article · Sat Sep 10 00:00:00 EDT 2011 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2011.07.017· OSTI ID:21592614

Diebold, Marc; Higgins, Chad; Parlange, Marc B ^[1]

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1. School of Architecture, Civil and Environmental Engineering (ENAC), Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne (Switzerland)

Highlights: {yields} A radial basis function based smoothing technique is introduced. {yields} It is more general and easier to implement compared to other techniques. {yields} With this technique, a combined immersed boundary and spectral method is developed. {yields} It is shown that the proposed method works better in terms of reducing the non-physical Gibbs oscillation. - Abstract: It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.

• OSTI ID: 21592614
• Journal Information: Journal of Computational Physics, Vol. 230, Issue 22; Other Information: DOI: 10.1016/j.jcp.2011.07.017; PII: S0021-9991(11)00436-0; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BOUNDARY ELEMENT METHOD
COMPUTER CALCULATIONS
COMPUTERIZED SIMULATION
CROSS SECTIONS
CYLINDERS
FUNCTIONS
INCOMPRESSIBLE FLOW
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
OSCILLATIONS
PERIODICITY
VISCOUS FLOW
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
FLUID FLOW
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
VARIATIONS