Ould-Salihi, M. L.; Cottet, G.-H.; El Hamraoui, M. Blending finite difference and vortex methods for incompressible flow computations. (English) Zbl 0993.76057 SIAM J. Sci. Comput. 22, No. 5, 1655-1674 (2001). The paper is devoted to numerical solution of nonstationary Navier-Stokes system on the base of coupling of finite difference and vortex methods. Actual variants of domain decomposition with overlapping subdomains are considered for problems with two or three space variables; Runge-Kutta or simpler Euler approximations with respect to time are used. The authors discuss applications of such methods to the driven cavity flow, to dipole-wall and ring-wall interactions, and to some other problems. They pay special attention to high-order interpolation formulas which are required to transfer information between the two methods. Very interesting numerical examples are presented; they include cases with large Reynolds number (up to \(10^5\)) and fairly rich grids (like \(1024^2\) or \(128^3\)). Reviewer: Evgenij D’yakonov (Moskva) Cited in 27 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76M23 Vortex methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs Keywords:nonstationary Navier-Stokes system; finite difference method; vortex method; Runge-Kutta scheme; Euler scheme; dipole-wall interaction; ring-wall interaction; domain decomposition; overlapping subdomains; driven cavity flow; high-order interpolation formulas; large Reynolds number flow PDFBibTeX XMLCite \textit{M. L. Ould-Salihi} et al., SIAM J. Sci. Comput. 22, No. 5, 1655--1674 (2000; Zbl 0993.76057) Full Text: DOI