A Chebyshev Pseudospectral Multidomain Method for a Boundary-Layer Problem

✍ Scribed by Francesco Malara

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 461 KB
• Volume: 124
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0058

✦ Synopsis

We indicate by ͳD [Ͱ,ͱ] ϭ D [Ͱ] ʝ D [ͱ] the internal boundary between the Ͱth and the ͱth subdomain. This partition A multidomain pseudospectral method, which is based on Chebyshev polynomials expansions, is presented to solve an initialmust be such that any quantity remains of C ȍ -class in each boundary value problem in incompressible MHD, the tearing instasubdomain D [Ͱ] during the time interval of interest. Then, bility, in which a boundary layer is spontaneously generated inside a spectral method is used in each subdomain giving the the spatial domain. The method is based on a property of Chebyshev appropriate boundary conditions at the internal boundpseudospectral expansions which accurately describe functions aries. This kind of technique was used by Bonazzola and having strong gradients localized near one of the Chebyshev domain boundaries. A comparison with the results of a single-domain pseu-Marck [2] to describe the shock propagation in fluid dydospectral method is performed, showing that, in the considered namics; a moving internal boundary was placed at the case, the multidomain technique furnishes a higher accuracy keepshock location, at any time step; on this boundary the shock ing the truncation error to a lower level. Because of the steeper jump conditions were used as boundary conditions. This Chebyshev spectra lower aliasing errors are obtained during the nonlinear stage of the instability.