Stability of interpolation on overlapping grids

• Published in: Computers & fluids Vol. 25; no. 6; pp. 583 - 605
• Main Authors: Olsson, Fredrik, Petersson, N.Anders
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1996; Elsevier Science
• Subjects: Algorithms; Approximation theory; Boundary conditions; Computational methods; Computational methods in fluid dynamics; Convergence of numerical methods; Eigenvalues and eigenfunctions; Exact sciences and technology; Finite difference method; Fluid dynamics; Fundamental areas of phenomenology (including applications); Integration; Numerical analysis; Physics; Waveform analysis; Grids; Interpolation; Stability; One-dimensional calculations; Wave equations; Numerical simulation; Overlap; Cauchy problem
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/0045-7930(96)00020-5

The stability of interpolation for one-dimensional overlapping grids is considered. The Cauchy-problem for a second-order accurate centered finite difference approximation of u t = u x is analyzed on the semi-discrete level. The existence of generalized eigenvalues is demonstrated for some rare overlap parameters, in which cases the discretization of the corresponding strip problem is found to be unstable. It is demonstrated that the stability can be recovered by adding artificial dissipation to the equation. Numerical experiments on the strip problem show that when a second-order dissipation is used, the amount of dissipation necessary to cancel the spurious growth is O( h 2) in the absence of generalized eigenvalues and O( h) in their presence, where h is the grid size. It is also demonstrated that the accuracy is improved by using a fourth-order dissipation.