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Grid computing is a new framework for distributed computing that provides us a more advanced computing and memory resource sharing model for solving large scale computational problems. Under this environment, the challenging problem in computational fluid dynamics (CFD) can be resolved in an efficient way. However, the traditional solvers of partial differential equations (PDEs) using finite element method (FEM) are usually tight combinations of a mesh generator and a linear system solver, and thus not suitable for grid computing. In this paper, we present a newly designed grid-enabled client/server (CS) model for the 3D Stokes/Navier-Stokes problem on more complicated hybrid meshes. This paper mainly focuses on the construction of the client/server model under the grid environment, and how to apply it to the Stokes system.