Implicit multiblock euler computations using a preconditioned GMRES method

Abstract

This chapter presents the parallel implementation of a right, preconditioned GMRES algorithm applied to an implicit Euler solver for steady compressible flows. Two types of preconditioners: local line relaxation and polynomial techniques are studied. The multiblock method is parallelized by using PVM and implemented on a T3D Cray system. Numerical results are presented for transonic and subsonic flows. A static domain decomposition of the structured mesh is employed at the beginning of each calculation. The computational domain is divided into a number of subdomains called solution blocks. Two different partitioning strategies have been implemented, which cut the domain along one or two space directions. Each block is assigned to one processor and consists of a set of grid points surrounded by one layer of ghost cells that is used for the boundary conditions and for the communication among the subdomains. Each of the processors manages the data and calculates the solution in its block. The solution steps within the GMRES algorithm are evaluated globally with the data of all the subdomains. The most time-consuming operation in the method is the matrix–vector product, which is employed both into the GMRES algorithm and into the polynomial preconditioner.