A Spectral Embedding Method Applied to the Advection–Diffusion Equation

✍ Scribed by M. Elghaoui; R. Pasquetti

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 437 KB
• Volume: 125
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0108

✦ Synopsis

vation of the high accuracy feature, which is not addressed in [8,9], is generally not trivial, because embedding meth-In order to solve partial differential equations in complex geometries with a spectral type method, one describes an embedding ods usually produce solutions in Ͷ that are poorly regular approach which essentially makes use of Fourier expansions and at the boundary of the complex domain ⍀, thus inducing boundary integral equations. For the advection-diffusion equation, Gibbs phenomenon.

the method is based on an efficient ''Helmholtz solver,'' the accuracy

The goal of this study is to produce a highly accurate of which is tested by considering 1D and 2D Helmholtz-like probembedding method, applicable to conservation equations lems. Finally, the capabilities of the method are pointed out by considering a 2D advection-diffusion problem in a hexagonal such as the unsteady advection-diffusion equation or the geometry.