A wavenumber parallel computational code for the numerical integration of the Navier–Stokes equations

✍ Scribed by Giuseppe Passoni; Giancarlo Alfonsi; Giovanni Tula; Umberto Cardu

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 232 KB
• Volume: 25
• Category: Article
• ISSN: 0167-8191
• DOI: 10.1016/s0167-8191(99)00003-4

✦ Synopsis

A parallel computational code for the numerical integration of the Navier±Stokes equations has been developed. The system of partial dierential equations describing the non-steady ¯ow of a viscous incompressible ¯uid in three dimensions is considered and applied to the channel ¯ow problem. A mixed spectral-®nite dierence technique for the numerical integration of the governing equations is devised: Fourier decomposition in both streamwise and spanwise directions and ®nite dierences in the direction orthogonal to the solid walls are used, while a semi-implicit procedure of Runge±Kutta and Crank±Nicolson type is utilised for the advancement in time. A wavenumber parallelism is implemented for the execution of the calculations. Within each time step of integration, the computations are executed in two distinct phases, each phase corresponding to a dierent way of decomposing the computational domain, vertically and horizontally, respectively; in both phases of the whole calculation process, each portion of the computing domain is handled by a dierent CPU on a Convex SPP 1200/ XA parallel computing system. Results are presented in terms of performance of the calculation procedure with the use of 2,4,6 and 8 processors respectively and are compared with the single-processor performance. Also the accuracy of the parallel algorithm has been tested, by analysing the evolution in time of small amplitude disturbances of the mean ¯ow; a satisfactory agreement with the theoretical solution given by the hydrodynamic stability theory is found, provided that a given number of grid points in the y direction are present.