5 th ANKARA INTERNATIONAL AEROSPACE CONFERENCE AIAC-2009-026 17-19 August, 2009 - METU, Ankara AN IMPLEMENTATION OF PARALLEL GMRES SOLUTION METHOD ON A 3-D UNSTRUCTURED FLOW SOLVER Mustafa Kaya ∗ and Mehmet A. Ak ‡ T ¨ UB ˙ ITAK-SAGE Ankara, Turkey Ismail H. Tuncer § Middle East Technical University Ankara, Turkey ABSTRACT A parallel GMRES (Generalized Minimal Residual) solution method is implemented on a 3-D flow solver developed earlier. An open source parallel GMRES software, pARMS (parallel Algebraic Recursive Multilevel Solvers), is used. pARMS uses MPI library routines to run in a parallel computing environment based on distributed memory. The flow solver, SET3D, employs a vertex based finite volume method on hybrid, unstructured grids. It currently has Euler explicit and Gauss-Seidel implicit time integration schemes. In this study, pARMS software is integrated into SET3D, and validated against certain test cases. The results show that the performance of the pARMS integrated flow solver is significantly enhanced. INTRODUCTION The flow solver, SET3D, has been developed in T ¨ UB ˙ ITAK-SAGE for the solution of a wide range flow problems[4, 3, 5, 6]. Earlier versions of the solver was based on a cell-centered Finite Volume method. The cell-centered scheme has an advantage of eliminating the need for the control volume generation affords. However, it also brings the disadvantage of distributing the variables to the nodes which may cause additional numerical errors[5]. Recently, to improve accuracy of the solver, a cell-vertex scheme has been implemented. In the solver, first or second order accurate inviscid fluxes are evaluated by the Roe type flux difference splitting method. Although the Roe type inviscid fluxes are used in the flux evaluations, the flux Jacobians needed in implicit solutions are based on Steger-Warming type fluxes. The iterative implicit solution algorithm is based on a point Gauss- Seidel (GS) method, which requires considerably long computation times for 3-D flow solutions on high-resolution grids. In the present study, the node-based version of the solver is used. The GS solution algorithm is replaced by a parallel implementation of GMRES method provided by the open-source software, pARMS. Moreover, the flux Jacobians are now evaluated numerically. The integration of pARMS and the flow solver, SET3D is achieved by a system call. The communication needed for the data exchange between SET3D and pARMS programs is provided using the shared memory segments. NUMERICAL SOLUTION METHOD 3-D unsteady viscous or inviscid flows over a solid body are computed by solving the Euler or Navier-Stokes equations on an unstructured grid. The integral form of the 3-D flow equations is solved using the finite volume method based on the cell vertex values. The governing equation for a conservative variable, Q, in a volume, Ω, is given as ∂ ∂ t  Ω QdΩ+  S ˆ F · d ˆ S =  S ˆ G · d ˆ S (1) ∗ Dr. Researcher, Email: mkaya@sage.tubitak.gov.tr ‡ Dr. Researcher, Email: maliak@sage.tubitak.gov.tr § Prof. Dr. in Aerospace Engineering Department, Email: tuncer@ae.metu.edu.tr