A parallel spectral Fourier-Nonlinear Galerkin algorithm for simulation of turbulence

Abstract

We present a high-order parallel algorithm, which requires only the minimum interprocessor communication dictated by the physical nature of the problem at hand. The parallelization is achieved by domain decomposition. The discretization in space is performed using the Local Fourier Basis method. The continuity conditions on the interfaces are enforced by adding homogeneous solutions. Such solutions often have fast decay properties, which can be utilized to minimize interprocessor communication. In effect, the predominant part of the computation is performed independently in the subdomains (processors) or using only local communication. A novel element of the present parallel algorithm is the incorporation of a Nonlinear Galerkin strategy to accelerate the computation and stabilize the time integration process. The basic idea of this approach consists of decomposition of the variables into large scale and small scale components with different treatment of these large and small scales. The combination of the Multidomain Fourier techniques with the Nonlinear Galerkin (NLG) algorithm is applied here to solve incompressible Navier–Stokes equations. Results are presented on direct numerical simulation of two-dimensional homogeneous turbulence using the NLG method. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 699–715, 1997