Two-dimensional parallel solver for the solution of Navier–Stokes equations with constant and variable coefficients using ADI on cells
✍ Scribed by A. Averbuch; L. Ioffe; M. Israeli; L. Vozovoi
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 484 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0167-8191
No coin nor oath required. For personal study only.
✦ Synopsis
The paper proposed a new algorithm for the parallel solution of two-dimensional Navier-Stokes type equation with constant and non-constant coefficients which is mapped onto cell topology. This paper is a further development in the application of the local Fourier methods to the solutions of PDE's in multidomain regions. The extension of the above solution to problems with non-constant coefficients is suggested via spectral multidomain preconditioner. This approach is efficient when we have good local approximations in each subdomain. By dividing the computational domain into a large enough number of subdomains we can guarantee it. The new achievement here is that we are able to handle decomposition of the domain into cells that is the Ž . decomposed in both directions, x and y. An appropriate alternate direction implicit ADI scheme was developed. It enables the reduction of a 2-D problem to a collection of uncoupled 1-D ODE's. In effect, the 1-D solver becomes the basic routine to solve a 2-D problem using splitting of the differential operators by ADI. Detailed performance analysis is given where the issue of the Ž . communication among the domains processors is examined. We show that by using the Richardson method only local communication is required. The algorithm was implemented on w