Spectral element formulations on non-conforming grids: A comparative study of pointwise matching and integral projection methods

Date

2006-01-01

Author

Sert, Cüneyt

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Pointwise matching (PM) and integral projection (IP) methods are two widely used techniques to extend the classical weak formulations to include non-conforming grids. We present spectral element formulations on polynomial (p-type) and geometric (h-type) non-conforming grids using both the PM (also known as the Constrained Approximation) and IP (also known as the Mortar Element) methods. We systematically compare the convergence characteristics of PM and IP methods for diffusion, convection, and convection-diffusion equations. Consistency errors due to the non-conforming formulations of the diffusion equation result in convergence problems for the PM method using the maximum rule. Both non-conforming formulations for the unsteady convection operator result in eigenvalue spectrum with positive real values, causing convergence problems due to the consistency errors. However, small "physical" diffusion in the convection-diffusion equation eliminates these problems, resulting in spectral convergence for both methods. Encouraged by this, we present spectral element formulations for incompressible Navier-Stokes equations using PM and IP methods on p-type and h-type non-conforming grids, and demonstrate spectral convergence for unsteady and steady test cases. Results for two-dimensional lid-driven cavity flow at Re = 1000 are also presented. (c) 2005 Elsevier Inc. All rights reserved.

Subject Keywords

Physics and Astronomy (miscellaneous), Computer Science Applications

URI

https://hdl.handle.net/11511/40938

Journal

JOURNAL OF COMPUTATIONAL PHYSICS

DOI

https://doi.org/10.1016/j.jcp.2005.05.019

Collections

Department of Mechanical Engineering, Article

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Citation Formats

C. Sert, “Spectral element formulations on non-conforming grids: A comparative study of pointwise matching and integral projection methods,” JOURNAL OF COMPUTATIONAL PHYSICS, pp. 300–325, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40938.